Question

match each quadratic function to its graph.$f(x) = -x^2 - 5x - 4 = -(x + 4)(x + 1)$$g(x) = -x^2 + 2x - 1 = -(x - 1)^2$$h(x) = x^2 + 4$$k(x) = -x^2 - 3$$f(x) = -x^2 - 5x - 4$$g(x) = -x^2 + 2x - 1$$h(x) = x^2 + 4$$k(x) = -x^2 - 3$

Explanation:

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

This parabola opens upward (\(a=1>0\)) with y-intercept at \(y=4\). This matches the bottom-left graph.

Step2: Analyze \(k(x)=-x^2-3\)

This parabola opens downward (\(a=-1<0\)) with y-intercept at \(y=-3\), vertex at \((0,-3)\). This matches the top-left graph.

Step3: Analyze \(g(x)=-(x-1)^2\)

This parabola opens downward (\(a=-1<0\)) with vertex at \((1,0)\) (touches x-axis at \(x=1\)). This matches the top-right graph.

Step4: Analyze \(f(x)=-(x+4)(x+1)\)

This parabola opens downward (\(a=-1<0\)), x-intercepts at \(x=-4\) and \(x=-1\), vertex at \(x=\frac{-4-1}{2}=-2.5\). This matches the bottom-right graph.

Answer:

• Top-left graph: \(k(x) = -x^2 - 3\)
• Top-right graph: \(g(x) = -x^2 + 2x - 1\)
• Bottom-left graph: \(h(x) = x^2 + 4\)
• Bottom-right graph: \(f(x) = -x^2 - 5x - 4\)