SOLUTION: identify the vertex and the intercepts. F(x)= 1/4 (x^2 -16x +32), g(x)+ 1/2 (x^2 + 4x -2)

Question 185073This question is from textbook college algebra concepts and models
: identify the vertex and the intercepts. F(x)= 1/4 (x^2 -16x +32), g(x)+ 1/2 (x^2 + 4x -2) This question is from textbook college algebra concepts and models

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
identify the vertex and the intercepts.
F(x)= 1/4 (x^2^ -16x +32),
(1/4)(x^2 -16x + ?) = y-8
(1/4)(x^2 - 16x + 64) = y-8+16
(1/4)(x-8)^2 = y+8
----------------------
Vertex: (8,-8)
intercepts:
x-intercept: Let y = 0 and solve for x:
(1/4)(x^2 - 16x + 32) = 0
x^2 -16x + 32 = 0
x = [16 +- sqrt(16^2 - 4*1*32)]/2
x = [16 +- sqrt(128)]/2
x = [16 +- 8sqrt(2)]/2
x = [8 +- 4sqrt(2)]
x = 8 + 4sqrt(2) or x = 8 - 4sqrt(2)
---
y-intercept:
Let x = 0 ; then y = (1/4)32 = 8
---------

=======================================
g(x) = (1/2) (x^2^ + 4x -2)
(1/2)(x^2 + 4x +?) = y + 1
(1/2)(x^2 + 4x + 4) = y + 1 + 2
(1/2)(x+2)^2 = y + 3
----
Vertex:(-2,-3)
y-intercept:
Let x = 0, then y = (1/2)-2 = -1
---------------------
x-intercept
Let y=0, then (1/2)(x^2+4x-2) = 0
x^2 + 4x -2 = 0
x = [-4 +- sqrt(16 - 4*1*-2)]//2
x = [-4 +- sqrt(24)]/2
x = [-4 +- 2sqrt(6)]/2
x = [-2 +- sqrt(6)]
x = -2 + sqrt(6) or x = -2 - sqrt(6)
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Cheers,
Stan H.

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