Question

which graph shows solving $2x^2 - 8x + 5 = -x^2 + 4$ by graphing a system?

Explanation:

Step1: Split into system equations

Set $y=2x^2-8x+5$ and $y=-x^2+4$.

Step2: Identify parabola directions

For $y=2x^2-8x+5$, coefficient of $x^2$ is $2>0$, so it opens upward. For $y=-x^2+4$, coefficient of $x^2$ is $-1<0$, so it opens downward.

Step3: Match to graph

Only the leftmost graph has one upward-opening and one downward-opening parabola, matching the system.

Answer:

The first graph (leftmost option)