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Given the parent function f(x)= x^2, write in 3 different forms

 

a) In Vertex Form         f(x)= a(x-h)^2+k

b) In Standard Form    f(x)= ax^2+bx+c

c) In Factored Form     f(x)= a(x-r)(x-r)

 

The points on the graph were

 

(3,0)

(4,-1)

(5,0)

 Mar 26, 2020
 #1
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If you graph these three points and draw a parabole that passes through these points, you will see that

--  the vertex occurs at (4, -1) 

--  that the value of a must be 1:

a)  f(x)  =  1(x - 4)2 - 1

 

Multiplying this out:  (x - 4)2 - 1  =  x2 - 8x + 16 - 1  =  x2 - 8x + 15

b)  f(x)  =  1x2 - 8x + 15

 

Factoring:  x2 - 8x + 15  =  (x - 5)(x - 3)

c)  f(x)  =  1(x - 5)(x - 3)

 Mar 26, 2020

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