Intercept form of a quadratic equation

CK-125.45.7

Standards

• CCSS.MATH.CONTENT.HSA.SSE.B.3.AFactor a quadratic expression to reveal the zeros of the function it defines.• CCSS.MATH.CONTENT.HSA.SSE.B.3

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.*

• CCSS.MATH.CONTENT.HSA.CED.A.2Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Objectives

• Solve and graph a quadratic equation by factoring.

Example 1

Graph x ² -8x + 12 = f(x)Intercept form can be used if the quadratic can be easily factored.Find the x-intercepts

x ² -8x + 12 = 0• Looking for factors of 12 that add up to -8.• (x – 6) (x - 2) = 0• X = 6 and x = 2• (6, 0) and (2,0) are intercepts of the graph

• Using the intercepts, the vertex can be found.• Take the x-values of the

intercepts and average it, that is the x-value of the vertex.

• Solve for f(4).• f(4) = (4-6)(4-2) • f(4) = (-2)(2)• f (4) = -4• (4,-4) is the vertex

Example 2

• Graph

• Factor out -1/3

Example 2

• Graph

• Factor out a -1/3

• x-intercepts are (5,0) and (-1,0)Find the x-value of the vertex

•g(2) = 3•Vertex is (2,3)

Practice

• Graph x ² - 5x – 6 = f(x)

Example 3

• Graph 2x ² +11x +12 = h(x)

AC Method (when a is not 1)

(x+4)(2x+3) = h(x)

X-intercepts are (-4,0) and (-3/2,0)

Find the x-value of the vertex

(-4,0)(-3/2, 0)(-11/4, -25/8)

Practice

1) Graph 3x ² +16x +5 = f(x)

(3x +1) (x+5) = f(x)

(-5,0)(-1/3,0)(-8/3, -49/3)

Homework

• Khan Academy:• Solving quadratics by factoring

• Solving quadratics by factoring 2

CW

• 2.5 pg 53 reflection #2, 3, practice #5