Question

A parabola passes through the points (-2,8), (0,2), and (1,5). What function does the graph represent?

Answer 1

ANSWER

$y = 2 {x}^{2} + x + 2$

EXPLANATION

Let the function that represent the graph be:

$y = a {x}^{2} + bx + c$

The parabola passes through the points (-2,8), (0,2), and (1,5).

These points must satisfy the function.

For (-2,8), we have

$8= a{( - 2)}^{2} + b( - 2) + c$

This implies that that,

$4a - 2b + c = 8...(1)$

For (0,2), we have,

$2= a{( 0)}^{2} + b( 0) + c$

This implies that,

$c = 2$

For (1,5), we have

$5= a{( 1)}^{2} + b( 1) + c$

This implies that,

$a + b + c = 5...(2)$

Put c=2 into equation (1) and (2).

$4a - 2b + 2 = 8$

$4a - 2b = 8 - 2$

$4a - 2b = 6$

$2a - b = 3...(3)$

$a + b + 2=5$

$a + b =5 - 2$

$a + b = 3...(4)$

Add equation (3) and equation (4)

$3a = 6$

$a = 2$

Put a=2 into equation (4).

$2 + b = 3$

$b = 3 - 2 = 1$

Therefore the function is

$y = 2 {x}^{2} + x + 2$