Question

Which graph correctly solves the system of equations below? y = − x2 + 1 y = x2 − 4

A) quadratic graph opening up and quadratic graph opening down. They do not intersect.
B) quadratic graph opening up and quadratic graph facing down. They intersect at negative 2, negative 3 and 2, negative 3.
C) Two intercepting parabolas are shown, one facing downward and one facing upward. The downward facing parabola has a maximum at (0,1) and intercepts the x axis at 1 and negative 1. The upward facing parabola has a minimum at (0,-4) and intercepts the x axis at 2 and negative 2
D) two quadratic graphs opening up. They intersect at 0, negative 4.

Answer 1

C) Two intercepting parabolas are shown, one facing downward and one facing upward. The downward facing parabola has a maximum at (0,1) and intercepts the x axis at 1 and negative 1. The upward facing parabola has a minimum at (0,-4) and intercepts the x axis at 2 and negative 2

Explanation:

As shown in the attached, the graph of y = -x² +1 has its vertex at (0, 1) and opens downward. It crosses the x-axis at ±1. The graph of y = x² -4 has its vertex at (0, -4), opens upward, and crosses the x-axis at ±2. The description of this graph matches choice C.