Mid-Chapter Quiz
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Start by identifying a, b, and c in the given equation.
y-intercept: - 3
Axis of Symmetry: x=- 2
x-coordinate of the Vertex: - 2
Graph:
Let's begin by finding the y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex. Then, we will graph the function by making a table of values.
Consider the general expression of a quadratic function, f(x)= ax^2+ bx+ c, where a ≠ 0. Let's note three things we can learn from this equation.
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 | 2x^2+8x-3 | f(x)=2x^2+8x-3 |
|---|---|---|
| - 5 | 2( - 5)^2+8( - 5)-3 | 7 |
| - 4 | 2( - 4)^2+8( - 4)-3 | - 3 |
| - 2 | 2( - 2)^2+8( - 2)-3 | - 11 |
| 0 | 2( 0)^2+8( 0)-3 | - 3 |
| 1 | 2( 1)^2+8( 1)-3 | 7 |
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. Recall that the axis of symmetry is the line x=-2.
