Question

which graph shows $y = x^2 + 3x - 4$?

Explanation:

Step1: Find x-intercepts

Set $y=0$, solve $x^2+3x-4=0$.
Factor: $(x+4)(x-1)=0$, so $x=-4$ or $x=1$.

Step2: Find y-intercept

Set $x=0$, $y=0^2+3(0)-4=-4$.

Step3: Identify matching graph

The graph must cross x-axis at $(-4,0)$ and $(1,0)$, y-axis at $(0,-4)$.

Answer:

The third graph (rightmost one, crossing x-axis at -4 and 1, y-axis at -4)