Math: 1697ffcf

ID: 1697ffcf

(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Advanced Math)

Comment: Substitution is your friend.

Method 1: The point (a, a) gives us something to work with in the equation of the parabola.

(a) = 3(a)^2 - 14(a)

0 = 3a^2 - 15a

0 = 3a(a - 5)

a = 0 or 5

Since 0 is already taken in the given point (0, 0), the correct answer must be 5.

Method 2: Desmos can show you the answer directly just by graphing the two equations.

Since the point (0, 0) is given, a must represent the other point of intersection, and the correct answer is 5.

Method 3: You could also solve for x directly by substituting out y (from y = x) and then thinking of a as x once you knew the correct value.

(x) = 3x^2 - 14x

0 = 3x^2 - 15x

0 = 3x(x - 5)

x = 0 or 5

If x can be 0 or 5, and again, 0 is already taken, then a must be 5, so the correct answer is 5.