Math: 91e7ea5e

ID: 91e7ea5e 

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

Comment: Remember the basics, or learn them.

Method 1: The vertex form of a parabola is as follows: y = a(x - h)^2 + k, in which the point (h, k) is the vertex and "a" determines whether the graph points upward or downward and how fast it does so. This equation is not given on the SAT, but some questions require such background knowledge. In the question at hand, the point (4, -32) is the vertex. Because a parabola has a vertical axis of symmetry, we can use the points (0, 0) and (t, 0) to deduce that if the first 0 is 4 units from the vertex, so, too, must be the second x-value, t, just in the opposite direction.

4 + 4 = 8

The correct answer is 8.

Method 2: Plug in the equation to Desmos and look for the x-intercepts. One is at (0, 0), the given point, while the other is at (8, 0).

The correct answer must be 8.

Method 3: By far the worst option is to solve the equation algebraically, since more steps will introduce greater room for error. However, this method is okay as a backup. Substitute the point (t, 0) and solve.

(0) = 2((t) - 4)^2 - 32

0 = 2(t^2 - 8t + 16) - 32

0 = 2t^2 - 16t + 32 - 32

0 = 2(t^2 - 8t)

0 = t(t - 8)

t = 0 and t = 8

The correct answer is 8.