For each quadratic equation, find the:

a.) Roots
b.) y-intercept
c.) Vertex

y= 4(x-4)^2 +16

Question

For each quadratic equation, find the: 

a.) Roots 
b.) y-intercept 
c.) Vertex 

y= 4(x-4)^2 +16

anonymous · Answer

c?

e.cociuba · Answer

Ok so for the root part I can put it in my calc and find the roots. Give me a sec...

campbell_st · Answer

roots occur when y = 0, so let y = 0 and solev for x

so you have 

16 = 4(x -4)^2

divide by 4

4 = (x -4)^2

take the square root of both sides

$$\pm 2 = x - 4$$

add 4 to both sides 

$$x = -2 + 4....and.....x = 2 + 4$$

just simplify for your roots. 

y - intercept is when x = 0

and your equation is in vertex form 

$$y = (x - h)^2 + k$$

(h, k) is the vertex.... just match them up.

e.cociuba · Answer

Ok thanks that makes so much more sense!

e.cociuba · Answer

Ok so for the roots it's gunna be (2,6) Correct?

e.cociuba · Answer

SO the y-intercept is 80 correct?

campbell_st · Answer

the roots are correct. 

The y-intercept x = 0

$$y = ( 0 - 4)^2 + 16 = 16 + 16 $$

y intercept is y = 32

e.cociuba · Answer

y= 4(0-4)^2 +16: 
I put that in my calculator and got 80. I think u forgot to put the 4 in front of the parenthesis....