Question

n.7 match quadratic functions and graphs qce
match each quadratic function to its graph.
$f(x) = -x^{2} - 8x - 16 = -(x + 4)^{2}$
$g(x) = -2x^{2} + 20x - 50 = -2(x - 5)^{2}$
$f(x) = -x^{2} - 8x - 16$ $g(x) = -2x^{2} + 20x - 50$

Explanation:

Step1: Analyze \( f(x) = -(x + 4)^2 \)

The vertex form of a quadratic is \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex. For \( f(x) \), \( h = -4 \), \( k = 0 \), so the vertex is \((-4, 0)\). The coefficient \( a = -1 \) (negative, so parabola opens downward). The left graph has its vertex at \((-4, 0)\) and opens downward, so \( f(x) \) matches the left graph.

Step2: Analyze \( g(x) = -2(x - 5)^2 \)

For \( g(x) \), \( h = 5 \), \( k = 0 \), so the vertex is \((5, 0)\). The coefficient \( a = -2 \) (negative, opens downward). The right graph has its vertex at \((5, 0)\) and opens downward, so \( g(x) \) matches the right graph.

Answer:

\( f(x) = -x^2 - 8x - 16 \) matches the left graph.
\( g(x) = -2x^2 + 20x - 50 \) matches the right graph.