Question

Graph the equation y=−x²−8x−15 on the accompanying set of axes. You must plot 5 points including the roots and the vertex.

Answer 1

Answer:

Plot these points

(-3,0)

(-5,0)

(-4,1)

(-2,-3)

(-6,-3)

Step-by-step explanation:

Let find the zeros of the equation.

We can factor this equation.

Factor out the -1.

$- 1( {x}^{2} + 8x + 15)$

Factor using AC method

$- 1(x + 3)(x + 5)$

Set all the terms equal to zero.

$x + 3 = 0$

$x + 5 = 0$

$x = - 3$

$x = - 5$

So our x intercepts are -3,0 and -5,0.

To find our vertex, apply the -b/2a.

$\frac{8}{ - 2} = - 4$

Then

Substitute-4 for x.

$y = - {4}^{2} - 8( - 4) - 15 = 1$

So our vertex is at (-4,1).

Find some other points like -2 and -6.

To find -2, substitute-2 into the quadratic.

$y = - ( { - 2}^{2}) - 8( - 2) - 15 = - 3$

So -2,-3.

Since y=-4 is the axis of symmetry

-6,-3