Question

Write the equation of the parabola that passes through the points (
–
7,
–
7), (
–
5,0), and (
–
2,0).
Write your answer in the form y=a(x–p)(x–q), where a, p, and q are integers, decimals, or simplified fractions.

Answer 1

Answer:

  y = -0.7(x +5)(x +2)

Step-by-step explanation:

You want the equation of the parabola through points (-7, -7), (-5, 0), and (-2, 0).

X-intercepts

Two of the points are x-intercepts of the curve. They can be directly translated to the factors of interest. X-intercept 'p' gives rise to factor (x-p).

So far, we know the equation is ...

  y = a(x -(-5))(x -(-2)) = a(x +5)(x +2)

Scale factor

Using the third point, we can find the value of 'a'. Substituting for x and y gives ...

  -7 = a(-7 +5)(-7 +2) = a(-2)(-5) = 10a

  -0.7 = a . . . . . . . divide by 10

The equation is y = -0.7(x +5)(x +2).