Write the equation of the parabola that passes through the points (–7,–7), (–5,0), and (–2,0).

To find the equation of the parabola that passes through the points (-7,-7), (-5,0), and (-2,0), we can use the general form of a parabola equation, which is y = ax^2 + bx + c.

We can substitute the given points into this equation to form a system of three equations to solve for a, b, and c.

Substituting (-7,-7) into the equation gives us: -7 = 49a - 7b + c ---- (1)

Substituting (-5,0) into the equation gives us: 0 = 25a - 5b + c ---- (2)

Substituting (-2,0) into the equation gives us: 0 = 4a - 2b + c ---- (3)

We can solve this system of equations using substitution or elimination method. Let's use elimination.

Subtract equation (2) from equation (1): -7 = 24a - 2b ---- (4)

Subtract equation (3) from equation (2): 0 = 21a - 3b ---- (5)

Multiply equation (4) by 3 and equation (5) by 2 to make the coefficients of b the same: -21 = 72a - 6b ---- (6) 0 = 42a - 6b ---- (7)

Subtract equation (7) from equation (6): -21 = 30a a = -21/30 = -7/10

Substitute a = -7/10 into equation (2): 0 = 25(-7/10) - 5b + c 0 = -175/10 - 5b + c 0 = -17.5 - 5b + c 17.5 = 5b - c ---- (8)

Substitute a = -7/10 into equation (3): 0 = 4(-7/10) - 2b + c 0 = -28/10 - 2b + c 0 = -2.8 - 2b + c 2.8 = 2b - c ---- (9)

Subtract equation (9) from equation (8): 14.7 = 3b b = 14.7/3 = 4.9

Substitute a = -7/10 and b = 4.9 into equation (1): -7 = 49(-7/10) - 7(4.9) + c -7 = -34.3 + c c = -7 + 34.3 = 27.3

So, the equation of the parabola is y = -7/10x^2 + 4.9x + 27.3.