, 24.01.2020smilxess

# Write the equation for a parabola that has x-intercepts (−4.5, 0) and (−2.8, 0) and y-intercept (0, 37.8).

.

Step-by-step explanation:

Start with the two -intercepts. The two zeros of the quadratic equation for this parabola are:

, and.

(These are the -coordinates of the two -intercepts.)

By the factor theorem, (where is a real number) is a zero of a polynomial if and only if is a factor of that polynomial.

A quadratic equation is also a polynomial. In this case, the two zeros would correspond to the two factors

.

A parabola could only have up to two factors. As a result, the power of these two factor should both be one. Hence, the equation for the parabola would be in the form

,

where is the leading coefficient that still needs to be found. Calculate the value of using the -intercept of this parabola. (Any other point on this parabola that is not one of the two -intercepts would work.)

Since the coordinates of the -intercept are , and . The equation becomes:

.

Solve for :

.

Hence the equation for this parabola:

.

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Step-by-step explanation:

or

Step-by-step explanation:

we know that

The equation of a vertical parabola in factored form is equal to

where

a is a coefficient

x_1 and x_2 are the roots or x-intercepts of the quadratic equation

In this problem we have

substitute

Find the value of a

we have the y-intercept (0,37.8)

substitute the value of x and the value of y of the y-intercept in the equation and solve for a

so

Convert to expanded form

Do you know the answer?

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