Foundations 11 Quadratics Review

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Mathematics

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11th Grade

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Practice Problem

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Medium

Rochelle McAdam

Used 2+ times

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13 Slides • 48 Questions

Quadratic Functions Review

Vertex
Roots
Y-intercept

Label the parts on your screen

Parts of the Quadratic Function

Vertex

Also the Max or Min
Always write as an ordered pair (x,y)
When asked to write the value of the Max or Min, write the y value of the vertex

Domain & Range

The domain will always always always always be all real numbers (-inf, inf)
Range is the lowest point to the highest point (one of those points will always be infinity)
y>min or y<max

Axis of Symmetry

Vertical line that splits the function down the middle
Write your answer as x = k; k is the x value of the vertex

Multiple Choice

What is the green dot on the parabola called?

vertex

root

dot

minimum value

Multiple Choice

What is the green dashed line called?

roots or x-intercepts

parabola

axis of symmetry

line of dashes

Multiple Choice

Does this graph in the back have maximum or minimum value?

maximum

minimum

neither

both

Multiple Choice

A parabola has a vertex at (-3,2). Where is the axis of symmetry?

y = -2

x = 3

x = -3

y = 2

x - intercepts

Also called zeros or roots
There can be 2, 1, or no zeros
Write your answer as an ordered pair (x,y); y value will always be 0

Multiple Select

What are the zeros of the function? Choose all that apply.

x = 0

x = -3

x = -6

y = 18

Multiple Choice

Which answer choice describes y = -3x² +7x - 2 accurately?

opens up with a maximum

opens up with a minimum

opens down with a maximum

opens down with a minimum

Multiple Choice

What is another word for zeros?

y-intercepts

roots

vertex

axis of symmetry

Multiple Choice

Members of the math club launch a model rocket from ground level with an initial velocity of 96 ft/sec. This can be modeled with the function h(t) = -16t² + 96t. What is the range of the function?

0 ≤ y ≤ 145

y ≤ 145

0 ≤ x ≤ 6

All Reals

Multiple Choice

What are the x- intercepts?

x= 0 and x= -4

x= 0 and x= 4

y= 0

x= 2

Multiple Choice

How many solutions does this graph have?

one

two

no solutions

cannot be determined

Multiple Choice

What is the range of this function?

(- ∞,+∞)

[0, +∞)

[-2, +∞)

[2, +∞)

Multiple Choice

What does "a" control in a graph of f(x) = ax²+ bx+ c?

Opens up or down

Where the graph crosses at X-intercept

Where the graph crosses at Y-intercept

Multiple Choice

What form is the equation in?
y = 2x²-8x+7

Standard

Vertex

Factored

None of These

Multiple Choice

What is the y intercept for the equation:
y = -8x² + 3x - 7

(0, -8)

(0, 3)

(0, 7)

(0, -7)

Multiple Choice

What is the axis of symmetry for the following equation?
y=4x²-8x+9

x=-8

x=1

x=-1

x=2

Multiple Choice

Find the vertex of
f(x) = -x²- 4x + 12

(-2, 16)

(2, 0)

(2, 4)

(-2, 4)

Multiple Choice

Which form is the equation
y = -3(x-5)²+7 in?

Standard

Vertex

Factored

None of These

Multiple Choice

What is the vertex of
f(x) = 2(x - 5)² + 12

(-5, -12)

(5,-12)

(5, 12)

(-5, 12)

Multiple Choice

Identify the vertex and whether the graph opens up or down.

(-1, 4); opens up

(-1, 4); opens down

(1, 4); opens up

(1, 4); opens down

Multiple Choice

y = 5(x+2)(x-1)

Standard

Vertex

Factored

None of These

Multiple Choice

What are the
x-intercepts of the function
f(x)= (x - 2)(x + 3)?

x = - 2 or x = 3

x = 2 or x = -3

The are no real roots

x = 2 or x = 3

Multiple Choice

If I want to find out when an object hits the ground, I should _________.

Use x = (-b/2a) as my answer.

Set my equation = 0 and solve.

Replace x with 0 and evaluate.

Find the y-coordinate of the vertex.

Multiple Choice

y = (x-9)²+5
What is the vertex?

(-9,5)

(9,5)

(5,-9)

(-5,9)

Multiple Choice

What is the y-intercept of the following funtion
f(x) = -2x² +3x - 7

(0, -2)

(0, 3)

(0, -7)

(0, 7)

Quadratic Functions

Multiple Choice

When I want to find the maximum or minimum height of an object, I should_____.

Set the equation = 0 and solve.

Use x = (-b/2a) as my answer.

Substitute x = 0 into the equation.

Find the y-coordinate for the vertex.

Multiple Choice

What is vertex form of a quadratic function

ax² + bx + c

a(x - h)² + k

y - y₁= m(x - x₁)

Ax + By = C

Multiple Choice

Which of these is a quadratic function?

f(x) = 2x + 4

f(x) = -2x + 4

f(x) = 3x²

q(x) = 3x³ + 2x² - 4x + 9

Find the coordinate of the vertex in the function:

-2x²+8x-2

Some text here about the topic of discussion.

X- Value of the vertex: -b/2a

Multiple Choice

What is the vertex of the quadratic function:
y = x² - 6x + 11?

(3,2)

(-3,-2)

(-3,2)

(3,-2)

Transformations:

a - how wide or narrow the graph is and if it reflects
-h - x value of the vertex (always opposite)
k - y value of the vertex

Some text here about the topic of discussion.

y=a(x-h)²+k

Multiple Choice

Does
y = -4x²
have a maximum or minimum value?

maximum

minimum

Multiple Choice

Describe the transformation of y = (x - 4)²

Shift UP

Shift DOWN

Shift LEFT

Shift RIGHT

Multiple Choice

Describe the transformation of y = x² + 4

Shift UP

Shift DOWN

Shift LEFT

Shift RIGHT

Multiple Choice

Compare the function y = 0.3x² to the parent function y = x²

Wider

Narrower

Multiple Choice

Match the equation to its description.

Right 2 and up 2

Left 2 and up 2

Right 2 and down 2

Left 2 and down 2

Multiple Choice

Match the equation to its description.

Reflected over x, right 2 and up 1

Reflected over x, left 2 and up 1

Reflected over x, right 2 and down 1

Reflected over x, left 2 and down 1

Multiple Choice

If the blue is f(x)=x^2,then the red must be

g(x)=x²-5

g(x)=x²+5

g(x)=(x-5)²

g(x)=(x+5)²

Multiple Choice

If the blue is f(x)=x^2,the red must be

g(x)=(x+3)²

g(x)=(x-3)²

g(x)=x²+3

g(x)=x²-2

Multiple Choice

Does the equation open up or down?
Y = -3x² +7x - 2

down

both

neither

Multiple Choice

Find the vertex of
f(x) = -x²- 4x + 12

(-2, 16)

(2, 0)

(2, 4)

(-2, 4)

Solving a Quadratic Equation

One way to solve a quadratic equation is by factoring.

Break the quadratic equation into its linear factors.

Set each factor = 0 and solve.

Solve by the quadratic formula

all quadratic equations can be solved by the quadratic formula.

The part under the radical is called the discriminant.

It determines the number and type of solutions that the quadratic equation has.

Multiple Choice

Use the quadratic formula to find the solutions for

y = 2x² - 9x + 5

-8.14 and 6.14

-4.07 and 3.07

3.9 and 0.6

No solutions

Multiple Choice

How many solutions does the function have: $-3x^2+12x-1=0$

1 solution

2 solutions

No solution

Infinite solutions

Multiple Choice

Factor
k² -2k - 24

(k+4)(k-6)

(k+4)(k+6)

(k+6)(k-1)

(k-4)(k+6)

Multiple Choice

Solve by factoring
3m² - 2m = 1

{4/5, 3}

{1/5, 5/2}

{3/2, 1}

{-1/3, 1}

Multiple Choice

Solve by square roots
5x² = 80

{4, -4}

{4}

{5.831, -5.831}

{8.185, -8.185}

Multiple Choice

Solve Using the Quadratic Formula
x² + 4x - 40 = -8

-10 & -4

-4 & 10

-8 & 4

8 & -4

Multiple Choice

What should you do first in solving this equation?
x² + 6x - 13 = 3

Get factored form

Write down: a=1, b=6, c=-13

Make it equal 0 by subtracting 3 on each side

Type it all in a calculator.

Multiple Choice

Solve
4m² - 100 = 0

m=25, -25

m=96

m=5, -5

m=-96

Multiple Choice

The two solutions to
y = 2x² -x -3 are...

1 and 3/2

-1 and 3/2

-1 and -3/2

1 and -3/2

Multiple Choice

True or false:
The solution, root, x-intercept, and zero of a problem are all the same thing

True

False, because the solution and root are the same but the x-intercept and zero are different

False, because the x-intercept and root are the same but the zero and solution are different

False, they are all different

Quadratic Functions Review

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