
Vertex Form of Parabolas
Presentation
•
Mathematics
•
9th - 11th Grade
•
Medium
+3
Standards-aligned
John Phillips
Used 5+ times
FREE Resource
14 Slides • 27 Questions
1
Vertex Form of Parabolas
y=a(x−h)2+k
2
3 Forms of Quadratic Functions
Standard
Factored
Vertex
3
Fill in the Blanks
Type answer...
4
Fill in the Blanks
Type answer...
5
To find the x-intercepts (aka roots aka zeros)
We can factor!
We can use the quadratic formula!
We can even use complete the square (but probably won't because it's going to be used elsewhere!)
6
Multiple Choice
Which is another way of correctly expressing
(x - 3)(x - 3)?
(x2 - 32)
(x2 - 3)
(x + 3)(x - 3)
(x - 3)2
7
On the next slide
The next slide contains a factoring methods review video. Watch it only if you don't remember how to factor. Then proceed to the next slide (#9).
8
9
Multiple Choice
x2 − 7x − 18
(x − 9)(x + 2)
(x + 9)(x + 2)
(x − 9)(x - 2)
(x − 9)(x - 2)
10
Multiple Choice
Factor the expression: w2 - 15w - 54
(w + 6)(w - 9)
(w + 3)(w - 18)
(w + 2)(w - 27)
(w - 6)(w + 9)
11
Multiple Choice
Factor the expression: 10v2 + 11v - 8
(5v + 8)(2v + 1)
(v + 8)(v - 1)
(5v + 8)(2v - 1)
(10v - 8)(v + 1)
12
Making Connections
Ok, you know how to factor.
Now let's factor with purpose. First, we'll factor to SOLVE equations.
THEN, we'll factor to find the ROOTS of quadratic functions.
I hope you'll see it's essentially the same process.
13
14
15
Multiple Choice
Solve.
n2 - 5 = -4
n = ±√9
n = ±3
n = ±1
No real solution
16
Multiple Choice
What are the x-intercept/s of the function?
(3,0)
(-3,0)
(9,0) & (-9,0)
(-3, 0) & (3, 0)
17
Multiple Choice
What are the solutions to this equation? (x-3)(x+2)=0
x=3,-2
x=-3,2
x=2,3
x=3,2
18
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
19
Multiple Choice
What are the zeros of the quadratic function?
y = x2 - 2x - 15
x = -2
x = -15
x = -3
x = 5
x = 3
x = -5
x = 1
x = -16
20
Multiple Choice
What are the x-interepts for the graph of the function: y = x2 - 3x - 10
-5, 2
-5, -2
5, -2
5, 2
21
Vertex Form
(h, k) is the point we call the vertex
It is the maximum or minimum point for the parabola
You read it DIRECTLY from the equation
Aside: Does this parabola have x-intercepts?
22
x-intercepts?
No, this parabola does NOT touch the x-axis.
Therefore, we could say that it does not have any REAL roots
However, upon solving it, we would determine that it has IMAGINARY solutions...or roots...or zeros
More on this next week!
For now, watch the video on the next slide!
23
24
Converting to Vertex Form
Complete the Square
Remember this!
(2b)2
25
Multiple Choice
Which of the following equations matches standard form of a quadratic?
ax + by = c
y = a(x - h)2 + k
y = ax2 + bx + c
y = mx + b
26
Multiple Choice
In vertex form,
f(x) = a(x - h)2 + k
what does the h stand for?
the y-coordinate of the vertex
the x-coordinate of the vertex
the x-intercept
the y-intercept
27
Multiple Choice
The parabola y = 3(x + 1)2 + 3 has a vertex of
(3, 3)
(1, 3)
( - 1, 3)
(3, -1)
28
Multiple Choice
The parabola y = x2 - 2x + 4 will have a vertex of
(-1, 2)
(1, 2)
(-1, 3)
(1, 3)
29
Multiple Choice
Convert to vertex form:
y = x2 - 2x + 5
y = (x - 1)2 + 4
y = (x - 1)2 - 4
y = (x - 1)2 + 3
y = (x - 1)2 + 7
30
Multiple Choice
Convert to vertex form:
y = x2 + 8x + 2
y = (x + 4)2 - 14
y = (x + 4)2 - 6
y = (x + 4)2 - 18
y = (x + 4)2 + 6
31
Multiple Choice
Convert to vertex form:
y = x2 + 4x + 10
y = (x + 4)2 + 6
y = (x + 2)2 + 6
y = (x + 4)2 - 6
y = (x + 2)2 - 6
32
33
Multiple Choice
If a parabola has a vertex at (5, 0) and opens upward, how many x-intercepts will it have?
0
1
2
no way to tell
34
Multiple Choice
If a parabola has a vertex at (-3, 7) and opens downward, how many x-intercepts will it have?
0
1
2
no way to tell
35
36
Multiple Choice
Which equation matches the graph?
f(x)=(x−1)2+4
f(x)=(x+4)2−1
f(x)=−(x−1)2+4
f(x)=−(x+4)2−1
37
Multiple Choice
Which equations matches the graph above?
h(x)= (x+1)2−4
h(x)=−(x+1)2−4
h(x)=(x+4)2−1
h(x)=−(x+4)2+1
38
Multiple Choice
Which of the following is the correct equation for the given graph?
f(x) = (x - 2)2 - 1
f(x) = (x + 2)2 - 1
f(x) = -(x + 2)2 - 1
f(x) = -(x - 2)2 - 1
39
Multiple Choice
Which quadratic function is represented by the graph?
y = 2(x - 4)2 + 5
y = 2(x + 4)2 + 5
y = -2(x - 4)2 + 5
y = -2(x + 4)2 + 5
40
Multiple Choice
What is the equation of this graph?
f(x) = (x -5)2 + 1
f(x) = (x - 1)2 - 5
f(x) = (x + 1)2 - 5
f(x) = (x + 5)2 +1
41
Multiple Choice
What is the equation of this graph?
f(x) = (x -5)2 + 1
f(x) = (x - 1)2 - 5
f(x) = (x + 1)2 - 5
f(x) = (x + 5)2 +1
Vertex Form of Parabolas
y=a(x−h)2+k
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