Write the equation for the parabola that has x− intercepts (−4,0) and (1.5,0) and
y-intercept (0,−15).

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

Step-by-step 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

answer: domain and range mean all possible values of x and y that could be substituted to the inequality. a solution means all possible values that make the inequality statement true. so while the range is still all real numbers, the solution is the shaded area, for which y will always be greater than the line of the function.