Question

Write a quadratic function for each graph described.
The graph has x-intercept at -1 and 5/3, and the parabola pass through the point (5,40)

Answer 1

Answer:

$y=2x^2-\frac{4}{3}x-\frac{10}{3}$

Step-by-step explanation:

we know that

The roots of the quadratic function (x-intercepts) are

x=-1 and x=5/3

so

we can write the equation of the parabola as

$y=a(x+1)(x-\frac{5}{3})$

where

a is a coefficient

Remember that

The parabola pass through the point (5,40)

substitute the value of x and the value of y of the ordered pair in the quadratic equation and solve for a

x=5, y=40

$40=a(5+1)(5-\frac{5}{3})$

$40=a(6)(\frac{10}{3})$

$40=20a\\a=2$

substitute

$y=2(x+1)(x-\frac{5}{3})$

apply distributive property

$y=2(x^2-\frac{5}{3}x+x-\frac{5}{3})\\\\y=2(x^2-\frac{2}{3}x-\frac{5}{3})\\\\y=2x^2-\frac{4}{3}x-\frac{10}{3}$

see the attached figure to better understand the problem