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Chapter 9: Q. 516 (page 987)

In the following exercises, (a) rewrite each function in f(x)=ax-h2+kform and (b) graph it using properties.

f(x)=2x2-12x+7

Short Answer

Expert verified

(a) The function can be written as f(x)=2x-32-11.

(b) The graph of function, axis of symmetry x=3and vertex 3,-11shown.

Step by step solution

01

Step 1. Given information.

We have:

f(x)=2x2-12x+7

02

Part (a). Step 1. Rewrite the function in standard form. 

The function is fx=2x2-12x+7.

Add the same value to both sides:

f(x)=2x2-6x+7

Add 2脳9to the both sides:

f(x)+18=2x2-6x+9+7f(x)+18=2x-32+7f(x)=2x-32+7-18f(x)=2x-32-11

03

Part (b). Step 1. Find axis of symmetry.

The function is fx=2x2-12x+7.

Identify the coefficients by comparing the function with y=ax2+bx+c, it follows:

a=2,b=-12x=-b2ax=--122路2x=3

04

Part (b). Step 2. Find vertex.

The vertex of an up-down facing parabola of the form y=ax2+bx+c鈥�is xv=-b2a.

The parabola params are:

a=2,鈥�b=-12,鈥�c=7xv=-b2axv=--122路鈥�2xv=3

Substitute xv=3into the original function to find yv:

yv=-11

Therefore, the parabola vertex is:

3,鈥�-11

05

Part (b). Step 3. Find the graph using properties.

Plot the vertex 3,-11. Plot the axis of symmetry x=3.

Draw the smooth curve through the points. The points represents the function f(x)=2x2-12x+7:

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