y=-2x^2-8x+10

Question

Identify the following components of each quadratic function then graph the fuction

 y=-2x^2-8x+10

axis of symmetry 

vertex

y intercept

two other points

Answer 1

y = -2x² - 8x + 10

 

When we find the vertex, we will also find the axis of symmetry.  We will change the function into vertex form.

 

y = a(x - h)² + k

 

in which the vertex is in the form (h, k).

 

y = -2(x² + 4x + 4) +18

 

y = -2(x + 2)² + 18

 

If we expand this vertex form, we will get back the standard form.

 

 

Therefore, the vertex is (-2, 18).

 

The axis of symmetry is the x-coordinate of the vertex.  The axis of symmetry is x = -2

 

 

To find y-intercept, evaluate y when x=0.

 

 

To find two other points, which is the x-intercept, set y=0.  We can use the vertex form to find the x-intercepts.

 

-2(x + 2)² + 18 = 0

-2(x + 2)² = -18

 

(x + 2)² = 9

 

x + 2 = ± √(9)

x = -2 ± √(9)

 

x = -2 ± 3

 

x = -5     and    x = 1

 

 

The x-intercepts are (-5,0) and (1,0).