Intercept to Standard to Vertex Form

Presentation

•

Mathematics

•

10th - 12th Grade

•

Hard

•

CCSS

HSA.APR.A.1, HSA-SSE.B.3B, HSA-REI.B.4B

Standards-aligned

Mara Davis

Used 14+ times

FREE Resource

11 Slides • 17 Questions

Intercept to Standard to Vertex Form

Objectives

Use FOIL to go from Intercept (Factored) form to Standard form
Complete the Square (or other method) to go from Standard to Vertex form

Multiple Choice

What form of a quadratic equation would be easiest for finding the solutions?

Intercept form

Standard Form

Vertex form

Multiple Choice

What form of a quadratic equation would be easiest for finding the vertex?

Intercept form

Standard Form

Vertex form

Multiple Choice

What form of a quadratic equation would be easiest for finding the y-intercept?

Intercept form

Standard Form

Vertex form

FOIL

First ---- 3x and 2x
Outer ---- 3x and 3
Inner ----5 and 2x
Last ----5 and 3

Multiple Select

What are the FIRST terms

(2x - 5) (6x + 4)

Check 2 boxes, please.

-5

Multiple Select

What are the OUTER terms

(2x - 5) (6x + 4)

Check 2 boxes, please

-5

Multiple Select

What are the INNER terms

(2x - 5) (6x + 4)

Check two boxes, please

-5

Multiple Select

What are the LAST terms

(2x - 5) (6x + 4)

Check 2 boxes, please

-5

Multiple Choice

Please rewrite

(2x - 5) (6x + 4)

in Standard Form (FOIL then combine like terms)

$12x^2-22x+20$

$12x^2+22x+20$

$12x^2-22x-20$

$12x^2+22x-20$

Multiple Choice

Please FOIL to rewrite

(x - 7) (x - 2)

in Standard Form (FOIL then combine like terms)

$x^2-9x+14$

$x^2+9x+14$

$x^2-9x-14$

$x^2+9x-14$

Standard to Vertex Form

Recall the Vertex form (the bottom one)
h is the x-coordinate of the vertex
k is the y-coordinate of the vertex
a indicates the opening direction and stretch

Rewrite this equation in Vertex Form $y=-2x^2+8x-5$

Identify a, b and c
a=-2, b=8, c=-5
find h by plugging into $h=\frac{-b}{2a}$
$h=\frac{-8}{2\left(-2\right)}=\frac{-8}{-4}=2\ \left(note:\ 2\ negatives\ =\ positive\right)$
find k by plugging h into x in the original equation
$k=-2\left(2\right)^2+8\left(2\right)-5=3$

Rewrite this equation in Vertex Form...continued

a = -2, h = 2, k = 3
$y=-2\left(x-2\right)^2+3$

Rewrite this equation in vertex form $y=x^2-6x+8$

a=1, b=-6, c=8
$h=\frac{-\left(-6\right)}{2\left(1\right)}=3$
$k=\left(3\right)^2-6\left(3\right)+8=-1$
$y=\left(x-3\right)^2-1$

Rewrite this equation in vertex form $y=3x^2+12x+7$

a=3, b=12, c=7
$h=\frac{-12}{2\left(3\right)}=-2$
$k=3\left(-2\right)^2+12\left(-2\right)+7=-5$
$y=3\left(x+2\right)^2-5$

Fill in the Blanks

Please identify a $y=2x^2-16x+33$

Type answer...

Fill in the Blanks

Please find h

$y=2x^2-16x+33$

\left(h=\frac{-b}{2a}\right)

Type answer...

Fill in the Blanks

Please find k

$k\ =2\left(4\right)^2-16\left(4\right)+33$

Type answer...

Multiple Choice

Please find a, h and k

$y=4x^2+40x+98$

a = 4, h = -5, k = 2

a = -4, h = -5, k = -2

a = 4, h = -5, k = -2

Multiple Choice

Please find a, h and k

$y=-2x^2+4x+1$

a = -2, h = 1, k = 3

a = -2, h = -1, k = 3

a = -2, h = 1, k = -3

Multiple Choice

a=2, h=4, k=1.

What is the equation in vertex form?

$-2\left(x+4\right)^2+1$

$2\left(x-4\right)^2+1$

$2\left(x+4\right)^2+1$

$2\left(x-4\right)^2-1$

Multiple Choice

a=-1, h=5, k=-3.

What is the equation in vertex form?

$y=-\left(x-5\right)^2+3$

$y=\left(x-5\right)^2-3$

$y=-\left(x+5\right)^2+3$

$y=-\left(x-5\right)^2-3$

Multiple Choice

a=-3, h=-4, k=1.

What is the equation in vertex form?

$y=-3\left(x+4\right)^2-1$

$y=3\left(x-4\right)^2+1$

$y=-3\left(x-4\right)^2+1$

$y=-3\left(x+4\right)^2+1$

Intercept to Standard to Vertex Form

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