How do you graph #f(x)= -(x+4)^2 + 9#?

Question

Isaiah Anthony · Accepted Answer

see explanation.

The following points are necessary. #• " coordinates of vertex"# #• " x and y intercepts"# #• " shape of parabola. That is max / min"# The equation of a parabola in #color(blue)"vertex form"# is. #color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))# where (h ,k) are the coordinates of the vertex and a is a constant. #f(x)=-(x+4)^2+9" is in this form"# #"with " a=-1, h=-4" and " k=9# #rArrcolor(magenta)"vertex "=(-4,9)# #"since " a<0" then max turning point " nnn# #color(blue)"intercepts"# #x=0toy=-16+9=-7larrcolor(red)" y-intercept"# #y=0to-(x+4)^2+9=0# #rArr(x+4)^2=9# #rArrx+4=+-3# #rArrx=-1" or " x=-7larrcolor(red)"x-intercepts"# graph{-(x+4)^2+9 [-20, 20, -9.98, 10.02]}

Avery Alexander · Answer

undefined To graph $ f(x) = -(x+4)^2 + 9 $, follow these steps:

1. Identify the vertex, which is the point $(-4, 9)$.
2. Since the coefficient of $x$ is negative, the parabola opens downwards.
3. Plot the vertex $(-4, 9)$ on the coordinate plane.
4. Choose additional points to plot by selecting $x$-values on either side of the vertex and plugging them into the equation to find the corresponding $y$-values.
5. Connect the points to form the graph of the quadratic function.