Warm Up #2 Find the Product: a. (x – 5)2 b. 4(x +5)(x – 5) ANSWER A projectile, shot from the ground reaches its highest point of 225 meters after 3.2 seconds. For how many seconds is the projectile in the air? ANSWER 6.4 seconds

Worksheet 4.1 Answers

EXAMPLE 1 Graph a quadratic function in vertex form 14 Graph y = – (x + 2)2 + 5. STEP 1 Identify the constants a = – , h = – 2, and k = 5. 14 STEP 2 Plot the vertex (h, k) = (– 2, 5) and draw the axis of symmetry x = – 2.

EXAMPLE 1 Graph a quadratic function in vertex form STEP 3 Evaluate the function for two values of x. x = 0: y = (0 + 2)2 + 5 = 4 14 – You Choose x = 2: y = (2 + 2)2 + 5 = 1 14 – Plot the points (0, 4) and (2, 1) and their reflections in the axis of symmetry. Because a < 0, the parabola opens down. STEP 4 Draw a parabola through the plotted points.

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Graph the function. Label the vertex and axis of symmetry. 1. y = (x + 2)2 – 3 2. y = –(x – 1)2 + 5 a = 1 vertex is (-2 , -3) a = -1 vertex is (1 , 5) Line of Symmetry is x = 1 Line of Symmetry is x = -2 Choose x values 2 , 3 Choose x values -1 , 0 (2 , 4) and (3 , 1) (-1 , -2) and (0 , 1) Plot Symmetry Points Plot Symmetry Points (0 , 4) and (-1 , 1) (-3 , -2) and (-4 , 1)

EXAMPLE 3 Graph a quadratic function in intercept form Graph y = 2(x + 3)(x – 1). 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 –3 + 1 = –1 = y = 2(–1 + 3)(–1 – 1) = –8 So, the vertex is (–1, –8) and the x-intercepts are (-3, 0) and (1, 0)

5. y = (x – 3)(x – 7) 6. f (x) = 2(x – 4)(x + 1) Graph the function. Label the vertex, axis of symmetry, and x-intercepts. 5. y = (x – 3)(x – 7) 6. f (x) = 2(x – 4)(x + 1) x-intercepts: (3, 0) and (7, 0) x-intercepts: (4, 0) and (-1, 0) Vertex: x = (7 + 3)/2 = 5 Vertex: x = [4 + (-1)]/2 = 1.5 Vertex: y = (5 – 3)(5 – 7) = -4 Vertex: y = 2(1.5 – 4)(1.5 + 1) = -12.5 Vertex: (5 , -4) Vertex: (1.5 , -12.5) Line of Symmetry: x = 5 Line of Symmetry: x = 1.5

Change from intercept form to standard form 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(x2 – 8x + 5x – 40) Multiply using FOIL. = –2(x2 – 3x – 40) Combine like terms. = –2x2 + 6x + 80 Distributive property

Change from vertex form to standard form EXAMPLE 6 Change from vertex form to standard form Write f (x) = 4(x – 1)2 + 9 in standard form. f (x) = 4(x – 1)2 + 9 Write original function. = 4(x – 1) (x – 1) + 9 Rewrite (x – 1)2. = 4(x2 – x – x + 1) + 9 Multiply using FOIL. = 4(x2 – 2x + 1) + 9 Combine like terms. = 4x2 – 8x + 4 + 9 Distributive property = 4x2 – 8x + 13 Combine like terms.

GUIDED PRACTICE for Examples 5 and 6 Write the quadratic function in standard form. 9. y = –(x – 2)(x – 7) 11. f(x) = 2(x + 5)(x + 4) ANSWER ANSWER –x2 + 9x – 14 2x2 + 18x + 40 10. y = –3(x + 5)2 – 1 12. f(x) = –(x + 2)2 + 4 ANSWER ANSWER –3x2 – 30x – 76 –x2 – 4x

Classwork Assignment: WS 4.2 (1-29 odd)