Question

graph the equation $y = -x^2 - 4x + 5$ on the accompanying set of axes. you must plot 5 points including the roots and the vertex. using the graph, determine the equation of the axis of symmetry.
click to plot points. click points to delete them.

Explanation:

Step1: Find roots (y=0)

Set $-x^2 -4x +5 = 0$, multiply by -1: $x^2 +4x -5 = 0$. Factor: $(x+5)(x-1)=0$. Roots: $x=-5, x=1$. So points: $(-5,0), (1,0)$.

Step2: Find vertex x-coordinate

Use $x=-\frac{b}{2a}$. For $y=-x^2-4x+5$, $a=-1, b=-4$.
$x=-\frac{-4}{2(-1)} = -2$

Step3: Find vertex y-coordinate

Substitute $x=-2$ into equation:
$y=-(-2)^2 -4(-2)+5 = -4 +8 +5 =9$. Vertex: $(-2,9)$.

Step4: Find additional points

Choose $x=-4$: $y=-(-4)^2-4(-4)+5=-16+16+5=5$. Point: $(-4,5)$
Choose $x=0$: $y=-(0)^2-4(0)+5=5$. Point: $(0,5)$

Step5: Find axis of symmetry

Axis of symmetry is $x =$ vertex x-coordinate: $x=-2$

Answer:

Plotted points: $(-5,0), (-4,5), (-2,9), (0,5), (1,0)$
Equation of the axis of symmetry: $x=-2$