The equation of a parabola with a vertical axis of symmetry is y= 14c(x-h)^2+k. How can you find the values of h, k, and c?
Equation: y= 132x^2-3 Graph:
Practice makes perfect
We want to write the equation of a parabola with vertex (0,- 3) and focus (0,5). Because the x-coordinate for the vertex and the focus is 0, the axis of symmetry of the parabola is the vertical line x=0.
Equation:& y=1/4 c(x- h)^2+ k
Vertex:& ( h, k)
Focus:& ( h, k+ c)
Since the vertex is ( 0, - 3), we have that h= 0 and k= - 3. Furthermore, we know that the y-coordinate of focus is 5.
5 = k+ c
Let's substitute - 3 for k in the above equation, and solve for c.
We can now write the equation of the parabola.
y=1/4( 8)(x- 0^2)+( - 3) ⇔ y=1/32x^2-3
Next, let's graph the parabola. To do so, let's first make a table of values.
x
1/32x^2-3
y = 1/32x^2-3
- 12
1/32( -12)^2-3
1.5
- 8
1/32( - 8)^2-3
- 1
0
1/32( 0)^2-3
- 3
8
1/32( 8)^2-3
- 1
12
1/32( 12)^2-3
1.5
Now let's plot the points and connect them with a smooth curve.
