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5.2.1 – Vertex and Intercept Form

5.2.1 – Vertex and Intercept Form. Standard form is just one version to express a quadratic Tricky to use because we always must use the vertex formula Two alternative ways to also write the form of a quadratic. Vertex Form. Vertex Form ; y = a(x – h) 2 + k, where (h, k) is the vertex

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5.2.1 – Vertex and Intercept Form

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  1. 5.2.1 – Vertex and Intercept Form

  2. Standard form is just one version to express a quadratic • Tricky to use because we always must use the vertex formula • Two alternative ways to also write the form of a quadratic

  3. Vertex Form • Vertex Form; y = a(x – h)2 + k, where (h, k) is the vertex • If a > 0, opens up (vertex is a minimum) • If a < 0, opens down (vertex is a maximum) • Convenient since we now can find the vertex without having to use tricky formula • Still graph by finding a second point and using the concept of symmetry

  4. Example. Find the vertex from the following quadratics: • 1) y = 2(x – 5)2 + 4 • 2) y = -5(x + 2)2 – 10 • 3) y = (x + 1)2 + 9 • 4) y = 3x2 + 7.9 • 5) y = (x – π)2

  5. Example. Graph the following quadratic. • y = -2(x – 2)2 + 1 • Up or down? • Vertex? • Second point?

  6. Example. Graph the following quadratic. • y = (x – 3)2 - 1 • Up or down? • Vertex? • Second point?

  7. Example. Graph the following quadratic. • y = -(x – 2)2 + 3 • Up or down? • Vertex? • Second point?

  8. Remember, we can still use our calculators as well to plot these, regardless what form • Example. Using your calculator, plot the following function and determine the vertex. • y = 4(x + 3)2 - 1

  9. Application • In terms of a parabola, we can fit the model to the path objects sometimes travel • Using our calculators, we can determine info such as the maximum height

  10. Example. The leap of a dolphin out of water is given by the function y = -0.03(x – 14)2 + 9. Determine the following: • A) sketch the graph of the jump • B) Find the maximum height of the jump

  11. Assignment • Pg. 231 • 4-6, 10-12, 23-27 odd, 35-39 (may use your calculator)

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