5. Given the quadratic function x -8x+12=y, find the:a) axis of symmetrye) Graph the function on the grid at the end of this review sheet.b) vertexc) x-intercepts (if any)d) y-intercept

Answered: Given the quadratic function x²-8x+12%…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section: Chapter Questions

Problem 35RE

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Question

5. Given the quadratic function x -8x+12=y, find the:
a) axis of symmetry
e) Graph the function on the grid at the end of this review sheet.
b) vertex
c) x-intercepts (if any)
d) y-intercept

Expert Solution

Step 1

$W e a r e s o l v i n g t h e f i r s t t h r e e s u b p a r t s a n d f o r t h e n e x t s u b p a r t s p o s t t h e q u e s t i o n a g a i n a n d a l s o m e n t i o n t h e q u e s t i o n n u m b e r t o b e s o l v e d . Q u e s t i o n 5, G i v e n, T h e q u a d r a t i c f u n c t i o n x^{2} - 8 x + 12 = y$

Step 2

$P a r t (a) ∴ x^{2} - 8 x + 12 = y \Rightarrow y = x^{2} - 8 x + 12 B y c o m p a r i n g w i t h y = a x^{2} + b x + c; a = 1, b = - 8, c = 12 ∴ A x i s o f s y m m e t r y i s g i v e n b y \Rightarrow x = \frac{- b}{2 a} \Rightarrow x = \frac{- (- 8)}{2 (1)} \Rightarrow x = 4 ∴ A x i s o f s y m m e t r y i s x = 4 . P a r t (b) y = x^{2} - 8 x + 12 \Rightarrow y = x^{2} - 8 x + 16 - 16 + 12 \Rightarrow y = {(x - 4)}^{2} - 4 B y c o m p a r i n g w i t h y = a {(x - h)}^{2} + k h = 4, k = - 4 T h e v e r t e x (h, k) i s (4, - 4)$

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