h(x)=2x^2-3
⇕
h(x)=2(x- 0)^2 + (- 3)
We can see that h= 0 and that k=- 3. Therefore, the vertex is ( 0,- 3), and the axis of symmetry is x= 0. To graph the function we will make a table of values. Make sure to include x-values to the left and to the right of the axis of symmetry.
x
2x^2-3
h(x)=2x^2-3
- 2
2( - 2)^2-3
5
- 1
2( - 1)^2-3
- 1
1
2( 1)^2-3
- 1
2
2( 2)^2-3
5
Let's now draw the parabola that connects the obtained points and the vertex. We will also draw the axis of symmetry x=0, and the parent function f(x)=x^2.
From the graph above, we can note the following.
Both graphs open up.
Both graphs have the same axis of symmetry x=0.
The graph of the given function is narrower than the graph of the parent function.
The vertex of the given function, (0,- 3), is below the vertex of the parent function, (0,0).
From the graph and the observations above, we can conclude that the graph of h is a vertical stretch by a factor of 2 and a vertical translation down 3 units of the graph of f.
