Question

match each equation with its graph. (1 point)

:: ( y = x^2 + 7x + 3 )
:: ( y = -x^2 + 3x - 4 )

Explanation:

Step1: Analyze the parabola direction

For a quadratic equation \( y = ax^2+bx + c \), if \( a>0 \), the parabola opens upward; if \( a < 0 \), it opens downward.

• For \( y=x^{2}+7x + 3 \), \( a = 1>0 \), so it opens upward.
• For \( y=-x^{2}+3x - 4 \), \( a=- 1<0 \), so it opens downward.

Step2: Match with the graphs

• The upper graph (first graph) has a parabola opening upward (since it curves upwards), so it should match \( y=x^{2}+7x + 3 \).
• The lower graph (second graph) has a parabola opening downward (since it curves downwards), so it should match \( y=-x^{2}+3x - 4 \).

Answer:

• \( y = x^{2}+7x + 3 \) matches the upper graph (first graph).
• \( y=-x^{2}+3x - 4 \) matches the lower graph (second graph).