Intro to Quadratics

Presentation

•

Mathematics

•

9th Grade

•

Medium

•

CCSS

HSF.IF.C.7, HSF.IF.B.4, HSF-IF.C.7A

+17

Standards-aligned

SANTANA SPEAR

Used 9+ times

FREE Resource

3 Slides • 29 Questions

Intro to Quadratic Functions

Multiple Choice

The graph of a quadratic function is called a

Parabola

Vertex

Axis of Symmetry

Vertex Form

Multiple Choice

What is the quadratic parent function?

$y=x$

$y=10^x$

$y=x^2$

Multiple Choice

Is the graph of the equation y=2x² wider, narrower or the same width as the standard parabola y = x²?

wider

narrower

same

impossible to tell

Multiple Choice

Which quadratic would be the narrowest?

$f\left(x\right)=\frac{1}{2}x^2$

$f\left(x\right)=x^2$

$f\left(x\right)=3x^2$

$f\left(x\right)=5x^2$

Multiple Choice

If the blue graph is f(x) = x²

then the red must be...

g(x) = x²- 5

g(x) = x²+ 5

g(x) = (x - 5)²

g(x) = (x + 5)²

Multiple Select

What are the other names for the "solution(s)" to a quadratic equation?

**Select all that apply!**

root(s)

x-intercept(s)

zero(s)

y-intercept(s)

Multiple Choice

Use the graph to determine the X-intercepts:

(-1,0) and (-3,0)

(1,0) and (3,0)

(0,1) and (0,3)

(0,-1) and (0,-3)

Multiple Choice

How many zeros does this parabola have?

Multiple Choice

Use the graph to determine the solutions.

-1 and -3

1 and -3

1 and 3

-1 and 3

Multiple Choice

What is another name for the x-intercepts of a quadratic?

y-intercept

Zeros

x-axis

They don't have another name

Multiple Choice

What is this formula?

This is the speed of light formula.

This is the quadratic formula.

This is the zero product property.

This is scary.

Multiple Choice

Does this parabola have a minimum or maximum and what is its value?

minimum: 2

maximum: 2

minimum: 5

maximum: 5

Multiple Choice

Does this graph have a maximum or a minimum?

maximum

minimum

I am not sure.

neither

Multiple Choice

Determine the domain and range of the function

Domain: All real numbers

Range: All real numbers

Domain: x ≥ -4

Range: All real numbers

Domain: All real numbers

Range: y ≥ -4

Domain: -1 ≤ x ≤ 5

Range: y ≥ -4

Multiple Choice

What is the green dashed line called?

roots or x-intercepts

parabola

axis of symmetry

line of dashes

Multiple Choice

Which value is the vertex?

(-4, 0)

(-1, -9)

(0, -8)

(2, 0)

Multiple Choice

What is the equation for the axis of symmetry?

x = 2

x = 6

x = 3

x = 0

Multiple Choice

Use the picture to find the vertex and axis of symmetry:

Vertex (3,8) Axis x = 3

Vertex (3,8) Axis y = 3

Vertex (8,3) Axis x = 3

Vertex (8,3) Axis y = 3

Multiple Choice

What is the vertex of the quadratic function:

f(x) = x² - 6x + 11

Hint: Use Desmos

(3,2)

(-3,-2)

(-3,2)

(3,-2)

Multiple Choice

Use the picture to find the vertex and axis of symmetry.

Vertex: (8, 3); axis of symmetry: y=3

Vertex: (8, 3); axis of symmetry: x=3

Vertex: (3, 8); axis of symmetry: y=3

Vertex: (3, 8); axis of symmetry: x=3

Multiple Choice

What is the vertex for
f(x)=4(x-2)² + 3

(-2, 3)

(2,-3)

(4,3)

(2,3)

Multiple Choice

Which equation has a vertex of (-3, 4)?

y = 2(x+3)²+ 4

y = (x+3)² - 4

y = (x-3)² + 4

y = 2(x - 3)² + 4

Multiple Choice

A fountain shoots water in an arc over a lake that can be modeled by the graph of the equation y= -0.4x² + 8x where x is the horizontal distance (in feet) from the fountain base and y is the height (in feet) above the river. How high does the water go?

It goes 11.78 feet high

It goes 20 feet high

It goes 40 feet high

It goes 10 feet high

Multiple Choice

A raft is dropped from a helicopter 256 feet in the air above the ocean. Its approximate height, h, after t seconds is given by the function h(t) = -16t² + 256. How many seconds did it take the raft to hit the water?

-4

Multiple Choice

What is the initial (starting) height of an object following this path? h(t) = -16t² +20t + 6

-16 feet

0 feet

20 feet

6 feet

Multiple Choice

If the graph shows price vs profit, what is the maximum profit?

12,000

12,500

Multiple Choice

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation
s(t) = –16t² + 64t + 80.
What will be the object's maximum height?

2 ft

80 ft

144 ft

64 ft

Multiple Choice

A lizard is jumping across the water in search of food. The equation h = -12t² + 6t models the lizard's height in feet above the water t seconds after he jumps. How long after jumping is he back on the water?

0.1 seconds

0.25 seconds

0.50 seconds

0.75 seconds

1 second

Multiple Choice

If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h after t seconds is given by the equation
h(t) = -16t² +128t
When will the object reach its maximum height?

4 ft

0 seconds

0 ft

4 seconds

Intro to Quadratic Functions

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