Finding the Vertex with -b/2a

​1. Domain and Range

2. Axis of Symmetry

3. Vertex

4. Maximum or Minimum

5. Increasing, Decreasing

6. x-intercepts, zeroes, roots, solutions

7. y-intercept​

​What are key features of quadratic functions?

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​1. The Axis, or Line, of Symmetry is a vertical line that divides the parabola into two symmetrical parts.

2. There is a corresponding y-value on either side of the axis of symmetry​

3. Since the AOS is a vertical line, it has the form of a vertical line: x = #

4. To find the AOS algebraically, set x = -b/2a.​

5. y = 2x² - 12x + 15​

a = 2, b = -12, c = 15

x = -(b)/2a x = -(-12)/2(2)​

​x = 12/4 = 3

​Axis of Symmetry (AOS)

​

​NOTE: the Axis of symmetry (AOS) is the x-part of the vertex.

For an AOS of x = -4, you would expect to see a Vertex with (-4, y)​

Multiple Choice

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

• y = -2
• x = 3
• x = -3
• y = 2

Multiple Choice

Find the axis of symmetry for

f(x) = x²- 8x + 15. (calculate -b/2a, please!)

• x = -4

• x = 4

• y = 4

• y = -4

Multiple Choice

What's the axis of symmetry of y = 3x² - 6x + 4

• x=1

• x=-6

• x=2

• x=-1

​1. The vertex is the coordinate point of the maximum, or minimum, point of the parabola.

​

2. To find the verte​x algebraically, find the axis of symmetry by the formula:

x = -b/2a. Use that value as the x-value of the vertex. For the y-value, substitute the AOS x-value into the function equation.

​

​3. y = 2x² - 8x + 7

​a = 2, b = -8, c = 7 AOS = -(-8)/2(2) = 2

​

y = ​2x² - 8x + 7 = 2(2)² - 8(2) + 7 = -8+7 = -1

Vertex = (2, -1)​

​Vertex

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Multiple Choice

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

• (3,2)
• (-3,-2)
• (-3,2)
• (3,-2)

Multiple Choice

The graph of a quadratic function is called

• a line
• a hyperbola
• a parabola
• a cubic

Multiple Choice

Standard form of a quadratic equation

• y=x²
• y=ax²+bx+c
• y=mx+b
• y=x

Multiple Choice

The formula x = -b/2a is used to find

• the roots
• the x-value of the vertex AND the axis of symmetry

• the y-intercept
• the end behavior of the function

Multiple Choice

What is the vertex of the quadratic equation

y = 4x² - 6x + 11?

Find AOS first by x = -b/2a (this is the x-part of the vertex), then plug in your answer to find the y-part of the vertex.

• (4, -6)

• (3/4, 35/4)

• (-3/4, -35,4)

• (-3/4, 35/4)

Multiple Choice

Remember how to find the y-intercept?

What's the y-intercept of y = 3x²- 6x + 4

• (4,0)
• (-4,0)
• (0,-4)
• (0,4)

Multiple Choice

What is the vertex?
f(x)=x²-8x+3

• (-8, 3)
• (4, -13)
• (4, 0)
• (-4, 51)

​Congrats you are done!