Forms of Quadratics

​Forms of quadratic equations

3 forms of a quadratic equation

​Standard Form

y = ax² + bx + c

​Vertex Form

y = a(x - h)² + k

​Factored Form

y = a(x - p)(x - q)

Match

Match the following

• Standard Form

• Vertex Form

• Factored form

f(x) = 3x² + 4x - 5

g(x) = 4(x - 6)² +1

t(x) = (x + 3)(x - 2)

• f(x) = 3x² + 4x - 5

• g(x) = 4(x - 6)² +1

• t(x) = (x + 3)(x - 2)

​What part of the graph do we know from STANDARD FORM?

y = ax² + bx + c


Lets discover the answer to this question by looking at graphs in this form

Labelling

The quadratic equation is in STANDARD FORM

y = x² + 6x + 3

and is graphed on the right.

Label the coordinates for the x-intercepts, y-intercept and vertex

Drag labels to their correct position on the image

(-5.5, 0)

(-0.5, 0)

(0, 3)

(-3, -6)

Match

The quadratic equation is in STANDARD FORM

y = x² + 3x - 2

it is graphed on the right.

Find the coordinates for the x-intercepts, y-intercept and vertex

• x-intercept

• y-intercept

• vertex

(-35, 0) (0.5, 0)

(0, -2)

(-1.5, -4.25)

• (-35, 0) (0.5, 0)

• (0, -2)

• (-1.5, -4.25)

Multiple Choice

The x-intercepts for the quadratic equation below are (0.25, 0) (3.75, 0) do you see the x-intercepts in the equation?

y = x² - 4x + 1

• yes

• no

Multiple Choice

The vertex for the quadratic equation below is (2, -3).

Do you see the vertex (2, -3) in the equation?

y = x² - 4x + 1

• yes

• no

Multiple Choice

The y-intercept for the quadratic equation below is (0, 1).

Do you see the y-intercept (0, 1) in the equation?

y = x² - 4x + 1

• yes

• no

Multiple Choice

Given the quadratic equation: y = x² + 2x - 5

What part of the graph do you know from the equation in STANDARD FORM?

*what number(s) do you see in the equation

• y-intercept

  (0, -5)

• x-intercepts

  (-3.5, 0) (1.5, 0)

• vertex

  (-1, -6)

Hotspot

Point to the term that represents the

y-intercept.

Match

Match each quadratic equation to their y-intercept

• y = 3x² + 5x - 2

• y = -2x² - 7x + 5

• y = -7x² + 3x - 4

• y = -4x² - 2x + 3

• y = 5x² - 4x - 7

(0, -2)

(0, 5)

(0, -4)

(0, 3)

(0, -7)

• (0, -2)

• (0, 5)

• (0, -4)

• (0, 3)

• (0, -7)

​What part of the graph do we know from VERTEX FORM?

y = a(x - h)² + k

Lets discover the answer to this question by looking at graphs in this form.

Match

The quadratic equation in VERTEX FORM: y = (x + 3)² - 6

is graphed on the right.

Find the coordinates for the x-intercepts, y-intercept and vertex

• x-intercept

• y-intercept

• vertex

(-5.5, 0) (-0.5, 0)

(0, 3)

(-3, -6)

• (-5.5, 0) (-0.5, 0)

• (0, 3)

• (-3, -6)

Labelling

The graph of y = (x + 2)² - 6 is in VERTEX FORM and is graphed on the right.

Label the x-intercepts, y-intercept and vertex.

Drag labels to their correct position on the image

(-4.5, 0)

(0.5, 0)

(0, -2)

(-2, -6)

Multiple Choice

The x-intercepts for the quadratic equation below are (3, 0) and (7, 0).

Do you see the x-intercepts (3, 0) (7, 0) in the equation?

y = (x - 5)² - 4

• yes

• no

Multiple Choice

The y-intercept for the quadratic equation below is (0, 21).

Do you see the y-intercept (0, 21) in the equation?

y = (x - 5)² - 4

• yes

• no

Multiple Choice

The vertex for the quadratic equation is (5, -4).

Do you see the vertex (5, -4) in the equation?

y = (x - 5)² - 4

• yes

• no

Multiple Choice

Given the quadratic equation y = (x + 6)² - 1

What part of the graph do you know from the equation in VERTEX FORM?

*What number(s) do you see in the equation?

• x-intercepts

  (-7, 0) (-5, 0)

• vertex

  (-6, -1)

• y-intercept

  (0, 35)

Hotspot

Point to the terms that represent the vertex

Match

Match each quadratic equation to its vertex

• f(x) = (x - 3)² + 5

• g(x) = (x + 3)² + 5

• h(x) = (x - 3)² - 5

• j(x) = (x - 5)² + 3

• y = (x + 5)² - 3

(3, 5)

(-3, 5)

(3, -5)

(5, 3)

(-5, -3)

• (3, 5)

• (-3, 5)

• (3, -5)

• (5, 3)

• (-5, -3)

​What part of the graph do we know from FACTORED FORM?

y = a(x - p)(x - q)

Lets discover the answer to this question by looking at graphs in this form.

Labelling

The graph of y = (x - 1)(x - 3) is in FACTORED FORM and is graphed on the right.

Label the x-intercepts, y-intercept and vertex

Drag labels to their correct position on the image

(1, 0)

(2, -1)

(3, 0)

(0, 3)

Match

The quadratic equation in FACTORED FORM: y = (x + 3)(x - 1)

is graphed on the right

Find the coordinates for the x-intercepts, y-intercept and vertex

• x-intercepts

• y-intercept

• vertex

(-3, 0) (1, 0)

(0, -3)

(-1, -4)

• (-3, 0) (1, 0)

• (0, -3)

• (-1, -4)

Multiple Choice

The x-intercepts for the quadratic equation below are (6, 0) and (-2, 0)

do you see the x-intercepts (6, 0) (-2, 0) in the equation?

y = (x - 6)(x + 2)

• yes

• no

Multiple Choice

The y-intercept for the quadratic equation below is (0, -12)

do you see the y-intercept (0, -12) in the equation?

y = (x - 6)(x + 2)

• yes

• no

Multiple Choice

The vertes for the quadratic equation below is (2, -16)

do you see the y-intercept (2, -16) in the equation?

y = (x - 6)(x + 2)

• yes

• no

Multiple Choice

Given the quadratic equation y = (x - 1)(x + 5)

What part of the graph do you know from the equation in FACTORED FORM?

*What number(s) do you see in the equation

• x-intercepts

  (1, 0) (-5, 0)

• y-intercept

  (0, -5)

• vertex

  (-2, -9)

Hotspot

Point to the term(s) that represent the

x-intercept(s)

Match

Match each quadratic equation to its x-intercepts

• y = (x + 5)(x - 2)

• y = (x + 2)(x - 5)

• y = (x + 5)(x + 2)

• y = (x - 2)(x - 5)

(-5, 0) (2, 0)

(-2, 0) (5, 0)

(-5, 0) (-2, 0)

(2, 0) (5, 0)

• (-5, 0) (2, 0)

• (-2, 0) (5, 0)

• (-5, 0) (-2, 0)

• (2, 0) (5, 0)

Match

Match each quadratic equation to the part of the graph you know

• y = (x + 7)(x + 11)

• y = (x - 4)² + 2

• y = x² + 3x - 7

the x-intercepts

the vertex

the y-intercept

• the x-intercepts

• the vertex

• the y-intercept