Axis of Symmetry and Vertex, Vertex Form of a Quadratic Equation

Axis of Symmetry

The line that splits a quadratic equation at the point of symmetry is called

a

In the expression ax² + bx + c, which value determines how the parabola opens?

Vertex

What is the point at which the parabola begins to change direction?

Minimum

If a quadratic equation opens upward, is the vertex a maximum or minimum?

x

Is the axis of symmetry the x value of the vertex or the y value of the vertex

x = 2

What is the axis of symmetry for the quadratic equation x² - 4x + 6 = 0?

(2, 2)

What is the vertex for the quadratic equation x² - 4x + 6 = 0?

Minimum

Is the vertex for the quadratic equation x² - 4x + 6 = 0 a max or a min?

x = 0

What is the axis of symmetry for the quadratic equation y = x² + 2?

(0, 2)

What is the vertex for the quadratic equation y = x² + 2?

Down

Will the graph for the quadratic equation f(x) = -2x² + 8x - 3 open up or down?

x = -2

What is the axis of symmetry in the graph shown?

(-2, -1)

What is the vertex in the graph shown?

(0, 1)

What is the vertex in the graph shown?

x = -1

What is the axis of symmetry in the graph shown?

(-1, -4)

What is the vertex in the graph shown?

(0, -4)

What is the vertex in the graph shown?

(3,4)

What are the coordinates of the Vertex of

the function: f(x) = (x - 3)² + 4

(-5, -17)

What are the coordinates of the Vertex of

the function: f(x) = -2(x + 5)² - 17

(5, -17)

What are the coordinates of the Vertex of

the function: f(x) = 3(x - 5)² - 17

(-3, 4)

What are the coordinates of the Vertex of

the function: f(x) = (x + 3)² + 4

5

In the function f(x) = (x - 1)² + 5, the minimum value occurs when x is:

-8

In the function f(x) = (x + 4)² - 8, the minimum value occurs when x is:

-10

In the function f(x) = -(x + 3)² - 10, the maximum value occurs when x is:

13

In the function f(x) = -2(x - 6)² + 13, the maximum value occurs when x is:

f(x) = (x - 6)² - 29

Rewrite f(x) in vertex form by completing the square. f(x) = x² - 12x +7

f(x) = (x - 3)² - 4

Rewrite f(x) in vertex form by completing the square. f(x) = x² - 6x + 5

f(x) = (x - 6)² - 45

Rewrite f(x) in vertex form by completing the square. f(x) = x² - 12x - 9

f(x) = (x - 3)² - 20

Rewrite f(x) in vertex form by completing the square. f(x) = x² - 6x - 11

f(x) = (x + 5)² - 28

Rewrite f(x) in vertex form by completing the square. f(x) = x² +10x - 3

f(x) = -(x - 5)² + 33

Rewrite f(x) in vertex form by completing the square. f(x) = -x² +10x +8

f(x) = -(x + 7)² - 10

Rewrite f(x) in vertex form by completing the square. f(x) = -x² - 14x - 59

f(x) = 2(x - 4)² - 47

Rewrite f(x) in vertex form by completing the square. f(x) = 2x² - 16x - 15

f(x) = 3(x + 2)² - 1

Rewrite f(x) in vertex form by completing the square. f(x) = 3x² +12x + 11

f(x) = -3(x - 4)² + 7

Rewrite f(x) in vertex form by completing the square. f(x) = -3x² +24x - 41

f(x) = 2(x + 5)² - 37

Rewrite f(x) in vertex form by completing the square. f(x) = 2x² + 20x + 13

f(x) = (x - 1)² +6

Rewrite f(x) in vertex form by completing the square. f(x) = x² - 2x + 7

f(x) = (x + 2)² - 4

Rewrite f(x) in vertex form by completing the square. f(x) = x² + 4x

f(x) = (x + 3)² - 32

Rewrite f(x) in vertex form by completing the square. f(x) = 3x² +18x - 5

f(x) = -(x + 5)² + 24

Rewrite f(x) in vertex form by completing the square. f(x) = -x² - 10x - 1

f(x) = (x - 1)² - 6

Rewrite f(x) in vertex form by completing the square. f(x) = x² - 2x - 5