Question

I need the explanation to understand pleasey= -2(x-1)^2 - 5A.) Identify the coefficients (a, h, and k) B.) Tell whether the graph opens up or opens down. C.) Find the vertex. Write as a coordinate. D.) Find the axis of symmetry. Write as an equation. E.) Find two more points on the graph. You can choose what x - values to use. Write your points as coordinates (x, y).

Answer 1

y= -2(x-1)^2 - 5



A.) Identify the coefficients (a, h, and k)



B.) Tell whether the graph opens up or opens down.



C.) Find the vertex. Write as a coordinate.



D.) Find the axis of symmetry. Write as an equation.



E.) Find two more points on the graph. You can choose what x - values to use. Write your points as coordinates (x, y).

Part a) we have a quadratic equation (vertical parabola) written in vertex form

y=a(x-h)^2+k

where

a is the leading coefficient

(h,k) is the vertex

in this problem

a=-2

(h,k)=(1,-5)

so

h=1

k=-5

Part b) the graph open downward (because a is negative)

Part c) the vertex is the point (1,-5) see the part a

Part d) Axis of symmetry

the axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex

so

x=h

we have

h=1

therefore

x=1

Part e) Find two points

For x=0

substitute

y= -2(0-1)^2 - 5

y=-7

First point (0,-7)

For x=1

y= -2(1-1)^2 - 5

y=-5

the second point is (1,-5) -----> is the vertex

For x=2

y= -2(2-1)^2 - 5

y=-7

the point is (2,-7)