Intercept to Standard to Vertex Form

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.

• 6x

• 4

• 2x

• -5

Multiple Select

What are the OUTER terms

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

Check 2 boxes, please

• 6x

• 4

• 2x

• -5

Multiple Select

What are the INNER terms

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

Check two boxes, please

• 6x

• 4

• 2x

• -5

Multiple Select

What are the LAST terms

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

Check 2 boxes, please

• 6x

• 4

• 2x

• -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 Blank

Please identify a $y=2x^2-16x+33$  

Fill in the Blank

Please find h

 $y=2x^2-16x+33$  

 $\left(h=\frac{-b}{2a}\right)$  

Fill in the Blank

Please find k

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

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?

•  $y=-3\left(x+4\right)^2-1$ 

•  $y=3\left(x-4\right)^2+1$ 

•  $y=-3\left(x-4\right)^2+1$ 

•  $y=-3\left(x+4\right)^2+1$