a The function is given in the graphing form. Choose five points for the table. Be sure to include point with the x-coordinate of the vertex within them. Plot these points and connect them with a smooth curve.
B
b When a quadratic function is given in a graphing form, f(x) = a(x-h)^2 + k, its vertex is the point (h,k).
C
c Substitute 100 and -15 for x in the given formula, one number at a time.
A
aTable: See solution.
Graph:
x-intercepts: (-1,0) and (3,0) y-intercepts: (0,6)
Next, recall that the general expression of a quadratic function in a graphing form is f(x)=a(x-h)^2+k, where a ≠0. Let's note three things we can learn from this equation.
The parabola opens downward if a< 0 and upward if a > 0.
f(x) = -2(x-1)^2+8
Looking at the given function we have a = -2, h = 1, and k = 8. Let's use these values to determine the mentioned properties of a parabola.
Since a = -2, we have a< 0 and the parabola opens downwards.
Now, let's make a table of values using five points. We want the center point to be the vertex and the remaining points to be symmetric on either side of it. We know that the points will be symmetric if the x-coordinates are equidistant from the axis of symmetry.
x
- 2(x-1)^2 + 8
f(x)=- 2(x-1)^2 + 8
- 1
- 2( -1-1)^2 + 8
0
0
- 2( 0-1)^2 + 8
6
1
- 2( 1-1)^2 + 8
8
2
- 2( 2-1)^2 + 8
6
3
- 2( 3-1)^2 + 8
0
Finally, we will graph the function by plotting the points from the table. Because the graph of a quadratic function is a parabola, we will connect them with a smooth curve.
Now, notice that among the chosen points we have two x-intercepts and a y-intercept. Let's list these points.
cc
x-intercepts & y-intercept
(-1,0), (3,0) & (0,6)
b When a quadratic function is given in a graphing form, f(x)=a(x-h)^2+k, its vertex is the point (h,k). Let's identify the values of h and k in the given function.
f(x) = -2(x-1)^2+8
Looking at the given function we have h = 1, and k = 8. Therefore, point (1, 8) is the vertex.
c To find the values of f(100) and f(-15), we will substitute 100 and -15 for x in the given formula, one number at a time. Let's start by substituting 100 for x.
