Practice Test
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Start by identifying a, b, and c in the given equation.
Choose five points for the table. Include the x-coordinate of the vertex found in Part A and use points from either side of the vertex for the remainder.
Plot the points from Part B and connect them with a smooth curve.
y-intercept: - 7
Axis of Symmetry: x=- 2
x-coordinate of the vertex: - 2
Example Table:
| x | f(x)=x^2+4x-7 |
|---|---|
| - 6 | 5 |
| - 4 | - 7 |
| - 2 | - 11 |
| 0 | - 7 |
| 2 | 5 |
Consider the general expression of a quadratic function, y= ax^2+ bx+ c, where a ≠0. Let's note three things we can learn from this equation.
a= 1, b= 4
Identity Property of Multiplication
Calculate quotient
The equation of the axis of symmetry is x=- 2 and the x-coordinate of the vertex is - 2.
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 | x^2+4x-7 | f(x)= x^2+4x-7 |
|---|---|---|
| - 6 | ( - 6)^2+4( - 6)-7 | 5 |
| - 4 | ( - 4)^2+4( - 4)-7 | - 7 |
| - 2 | ( - 2)^2+4( - 2)-7 | - 11 |
| 0 | 0^2+4( 0)-7 | - 7 |
| 2 | 2^2+4( 2)-7 | 5 |
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.
