Find the equation of the following quadratic, in vertex form f(r) = a(x – h) + k.6+-6 -5 -4 -3 -2 -1-2Previewf(x)=

Answered: Find the equation of the following…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Related questions

Question

Find the equation of the following quadratic, in vertex form f(r) = a(x – h) + k.
6+
-6 -5 -4 -3 -2 -1
-2
Preview
f(x)=

Expert Solution

Step 1

Given graph is

To find: The equation of the following quadratic in vertex form $f (x) = a {(x - h)}^{2} + k$

Step 2

Explanation:

From given graph we have the vertex point $(h, k) = (- 3, - 1)$ and we also have one point $(x, y) = (- 4, - 3)$ on the graph

Equation of the quadratic function is

$f (x) = a {(x - h)}^{2} + k \Rightarrow f (x) = a {(x - (- 3))}^{2} + (- 1) [∵ (h, k) = (- 3, - 1)] \Rightarrow f (x) = a {(x + 3)}^{2} - 1 . . . . . . (1) W e h a v e p o i n t (x, y) = (- 4, - 3) \Rightarrow - 3 = a {(- 4 + 3)}^{2} - 1 \Rightarrow - 3 = a {(- 1)}^{2} - 1 \Rightarrow - 3 = a - 1 \Rightarrow a = - 2 S u b s t i t u t e a v a l u e i n e q u a t i o n (1) ∴ f (x) = - 2 {(x + 3)}^{2} - 1$