Question

Write a quadratic function in intercept form whose graph passes through the points (-5,0)(-1,0) and (-7,-24)

Answer 1

Step-by-step explanation

The intercept-form of a quadratic function is as follows:

y = a(x - p)(x - q)

Now, as the roots are (-5,0)

Since the parabola passes through the point (−5,0), then 0=25a−5b+c

Since the parabola passes through the point (−1,0), then 0=a−b+c.

Since the parabola passes through the point (−7,−24), then −24=49a−7b+c.

Thus, we have obtained the following system:

Solving it we get that a=−2, b=−12, c=−10.

Thus, the equation of the parabola is y=(−2x−10)(x+1)