# A function whose graph is a parabola with vertex ( 1 , − 2 ) and passes through the point ( 4 , 16 ) ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 3.1, Problem 43E
To determine

## To Find: A function whose graph is a parabola with vertex (1,−2) and passes through the point (4,16)

Expert Solution

the equation of parabola is:

f(x)=3(x3)2+4=3x2+18x23

### Explanation of Solution

Given: The vertex is (1,2)

Points through which the parabola passes (4,16)

Calculation:

A quadratic function f(x)=ax2+bx+c is expressed in standard from as: f(x)=a(xh)2+k

Here, Compare the vertex (h,k)= (1,2) with standard form of the equation of parabola with points (4,16) .

f(x)=a(xh)2+k16=a(41)2+(2)         [put 1 for h,2 for k and 4 for x and 16 for f(x)]16=a9218=a92=a

Therefore, the equation of parabola is:

f(x)=2(x1)22=2x24x

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