Math: Advanced Math

SAT Question of the Day for October 26, 2026

A parabola is defined by

y = f(x)

where

f(x) = a(x - 3)^2 - 7

for some positive constant

a

. The function

g(x) = f(x - 11) + 4

is also a parabola. What is the vertex of

g

A. $(14, -3)$ Correct answer
B. $(-8, -3)$
C. $(14, -11)$
D. $(-8, -11)$

86% answered correctly.

Explanation

The vertex of

f

is at

(3, -7)

. Replacing

x

with

x - 11

shifts the parabola

11

units to the right, moving the

x

-coordinate from

3

3 + 11 = 14

. Adding

4

shifts the parabola up

4

units, moving the

y

-coordinate from

-7

-7 + 4 = -3

. The new vertex is

(14, -3)

. The vertex

(-8, -3)

incorrectly subtracts

11

from the

x

-coordinate instead of adding it. The vertex

(14, -11)

correctly shifts right but subtracts

4

instead of adding. The vertex

(-8, -11)

applies both shifts in the wrong direction.

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Explanation

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