Graphing a Quadratic Function
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Graph the parabola. $$y = -4x^2 + 5$$ Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph-a-function button.
This question includes visual content: A Cartesian coordinate plane with an x-axis ranging from -12 to 12 and a y-axis ranging from -12 to 12. Next to the graph is an interactive tool containing icons for erasing, pencil (drawing), curve plotting, grid settings, an undo button (arrow), and a clear button (X).
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Hi Imani, let's graph this parabola together. We need to find five specific points: the vertex, and two points on each side of it.
Graphing $y = -4x^2 + 5$
This equation is in vertex form, where the x squared term is isolated. Since there is no x term, the vertex is at an x coordinate of zero.
Comparing our equation to the vertex form, h is zero and k is five. So, our vertex is at the point zero, five.
Next, let's find two points to the right of the vertex by choosing x equals one and x equals two.
| x | y |
|---|---|
| 0 | 5 |
| 1 | ? |
| 2 | ? |
When x equals one, we calculate y as negative four times one squared plus five, which is negative four plus five, giving us one.
When x equals two, we have negative four times two squared plus five. That's negative four times four, which is negative sixteen, plus five, resulting in negative eleven.
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