Quick Write Write down the 2 formats we have learned for quadratics Under each format, write down all the things you can get from that format.

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Graph each function. Label the vertex and axis of symmetry.

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Presentation transcript:

Quick Write Write down the 2 formats we have learned for quadratics Under each format, write down all the things you can get from that format.

Review Multiply these together:

INTERCEPT FORMAT Section 4-2

Objectives I can find the solutions, axis of symmetry, and vertex point from Intercept Format I can graph a quadratic from Intercept Format I can convert Intercept Format to Standard Format

Intercept Format

Graphing Steps Find p and q Calculate AOS Calculate Vertex using AOS x-value Calculate y-intercept Let x = 0

EXAMPLE 3 Graph a quadratic function in intercept form Graph y = 2(x + 3) (x – 1). SOLUTION STEP 1 Identify the x - intercepts. Because p = – 3 and q = 1, the x - intercepts occur at the points (– 3, 0) and (1, 0). STEP 2 Find the coordinates of the vertex. x = p + q 2 – = – 1= y = 2(– 1 + 3)(– 1 – 1) = – 8

EXAMPLE 3 Graph a quadratic function in intercept form STEP 3 Draw a parabola through the vertex and the points where the x - intercepts occur.

GUIDED PRACTICE Graph the function. Label the vertex, axis of symmetry, and x - intercepts. 5. y = (x – 3) (x – 7) SOLUTION STEP 1 Identify the x - intercepts. Because p = 3 and q = 7, the x - intercepts occur at the points (3, 0) and (7, 0). STEP 2 Find the coordinates of the vertex. x = p + q = 5= y = (5 – 3) (5 – 7) = – 4 So the vertex is (5, – 4)

GUIDED PRACTICE for Examples 3 and 4 STEP 3 Draw a parabola through the vertex and the points where the x - intercepts occur.

GUIDED PRACTICE for Examples 3 and 4 7. y = – (x + 1) (x – 5) SOLUTION STEP 1 Identify the x - intercepts. Because p = – 1 and q = 5, the x - intercepts occur at the points (– 1, 0) and (5, 0). STEP 2 Find the coordinates of the vertex. x = p + q 2 – = 2= y = – (2 + 3)(2 – 1) = 9 So the vertex is (2, 9)

GUIDED PRACTICE for Examples 3 and 4 STEP 3 Draw a parabola through the vertex and the points where the x - intercepts occur.

EXAMPLE 5 Change from intercept form to standard form Write y = – 2 (x + 5) (x – 8) in standard form. y = – 2 (x + 5) (x – 8) Write original function. = – 2 (x 2 – 8x + 5x – 40) Multiply using FOIL. = – 2 (x 2 – 3x – 40) Combine like terms. = – 2x 2 + 6x + 80 Distributive property

GUIDED PRACTICE for Examples 5 and 6 Write the quadratic function in standard form. 9. y = – (x – 2) (x – 7) y = – (x – 2) (x – 7) Write original function. = – (x 2 – 7x – 2x + 14) Multiply using FOIL. = – (x 2 – 9x + 14) Combine like terms. = – x 2 + 9x – 14 Distributive property

GUIDED PRACTICE for Examples 5 and y = – 7(x – 6) (x + 1) y = – 7(x – 6) (x + 1) Write original function. = – 7(x 2 + x – 6x – 6) Multiply using FOIL. = – 7(x 2 – 5x – 6) Combine like terms. = – 7x x + 42 Distributive property