Question

Write an equation in intercept form for the parabola which has x-intercepts of -7 and 8 and passes through the point (13, -5). And how do get the answer

Answer 1

To write the equation of the parabola in intercept form, we use the x-intercepts and a given point to determine the coefficient a. The resulting equation is y = -0.05(x + 7)(x - 8).

Step-by-step explanation:

To write the equation of a parabola in intercept form, given the x-intercepts of -7 and 8 and a point (13, -5) that it passes through, we start with the intercept form of a quadratic equation, which is y = a(x - p)(x - q), where p and q are the x-intercepts. The equation will thus have the form y = a(x + 7)(x - 8). To find the value of a, we substitute the coordinates of the given point (13, -5) into the equation and solve for a.

So, substituting the point (13, -5) gives -5 = a(13 + 7)(13 - 8). This simplifies to -5 = a(20)(5), and further to -5 = 100a. Solving for a gives us a = -5/100 or a = -0.05. The final equation of the parabola is y = -0.05(x + 7)(x - 8).