Question

Write the equation for the parabola that has x− intercepts (−4,0) and (1.5,0) and

y-intercept (0,−15).

Answer 1

y = 2.5(x +4)(x -1.5) = 2.5x^2 +6.25x -15

Explanation:

Each given zero corresponds to a factor that is zero at that point. Those factors are (x +4) and (x -1.5).

The y-intercept tells us the scale factor, the multiplier that is needed to make the function value be -15 at x=0.

y = a(x +4)(x -1.5) = a(0 +4)(0-1.5) = -6a

-15 = -6a

-15/-6 = a = 2.5

So, the quadratic is ...

y = 2.5(x +4)(x -1.5) = 2.5x^2 +6.25x -15

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"The equation" can be written in many different forms. The simplest, given the information here, is the factored form (also called "intercept form"). We have also shown "standard form" (US version). The "standard form" (UK version) is also known as vertex form:

y = 2.5(x +1.25)^2 -18.90625