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

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Step-by-step explanation:

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

(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

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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:

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Solve for :

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Hence the equation for this parabola:

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the transverse axis of a hyperbola is the line that contains the two vertices and the two focuses.

in this example (hyperbola of equation x^2/2 - y^2/4 = 1), the transverse axis is the  x-axis  . 

step-by-step explanation: