Question

Write an equation for a parabola with​ x-intercepts (-2,0) and (5,0) which passes through the point (1,-60)

Write the equation :

Answer 1

y=5(x+2)(x-5)

Explanation:

The strategy to solve such problems is to write down the general equation of a parabola and then use the given information to solve for the coefficients.

Here, we know that the parabola has x-intercepts at (-2,0) and (5,0). This means that the parabola goes through the points (-2,0) and (5,0). Let's use these points in the general equation of a parabola, which is:

y = ax^2 + bx + c

We get the following system of equations:

0 = -4a + 2b + c

0 = 25a + 5b + c

-60 = a + b + c

Solving this system of equations, we get:

a = -15

b = 10

c = 10

Therefore, the equation of the parabola is:

y = -15x^2 + 10x + 10