# A function whose graph is a parabola with vertex ( 3 , 4 ) and passes through the point ( 1 , − 8 )

### 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 44E
To determine

## To Find: A function whose graph is a parabola with vertex (3,4) and passes through the point (1,−8)

Expert Solution

the equation of parabola is:

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

### Explanation of Solution

Given: The vertex is (3,4)

Points through which the parabola passes (1,8)

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)=(3,4) with standard form of the equation of parabola with points (1,8) .

f(x)=a(xh)2+k8=a(13)2+4         [put 3 for h,4 for k and 1 for x and 8 for f(x)]8=a4+412=a43=a

Therefore, the equation of parabola is:

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

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