Verified answer

d/dx=0

this is done to find turning point

d/dx=

2x+8=0

2x=-8

x=-4

f(-4)=(-4^2) + 8(-4)=-16

hence the turning point is (-4,-16)

it will be a minimum as x^2 is positive that is it will have a U shape

then you can give any values to x to find the other points

you can also use the completing of squares method it will give the same answer

x^2+8x

=[x^2+8x+(8/2)^2-(8/2)^2]

=(x+4)^2-16

when y=-16

x+4=0

x=-4

turning point is (-4,-16)

Make a chart to graph the function, or complete the square to figure out what the function looks like when its graphed out. You'll notice that when y=0, 0=x^2 +8x = x(x+8), which means that your zeros of the parabola are at 0 and -8. You can also use the formula for line of symmetry x=(-b)/a to find out the x value of the turning point, and then to plug in x into the equation to find the y value of the turning point. And if you notice, the coefficient of x^2 is positive, so the parabola is concave up.

First, find x-intercepts:

x² + 8x = 0

x (x+8) = 0

x = 0, -8

So curve intersect x-axis at points (-8,0) and (0,0)

Now find vertex (located halfway between x-intercepts)

x = (-8+0)/2 = -4

f(-4) = 16 - 32 = -16

Vertex: (-4, -16)

So plot the points

(-8,0), (0,0), (-4, -16)

Draw a curve that passes through these 3 points.

Remember that vertex (-4, -16) is minimum point of curve