EXAMPLE 3 Graph a function of the form y = ax 2 + bx + c Graph y = 2x 2 – 8x + 6. SOLUTION Identify the coefficients of the function. The coefficients.

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EXAMPLE 3 Graph a function of the form y = ax 2 + bx + c Graph y = 2x 2 – 8x + 6. SOLUTION Identify the coefficients of the function. The coefficients are a = 2, b = – 8, and c = 6. Because a > 0, the parabola opens up. STEP 1 STEP 2 Find the vertex. Calculate the x - coordinate. x = b2a b2a = (– 8) 2(2) –– = 2 Then find the y - coordinate of the vertex. y = 2(2) 2 – 8(2) + 6 = – 2 So, the vertex is (2, – 2). Plot this point.

EXAMPLE 3 Graph a function of the form y = ax 2 + bx + c STEP 3Draw the axis of symmetry x = 2. STEP 4Identify the y - intercept c, which is 6. Plot the point (0, 6). Then reflect this point in the axis of symmetry to plot another point, (4, 6). STEP 5 Evaluate the function for another value of x, such as x = 1. y = 2(1) 2 – 8(1) + 6 = 0 Plot the point (1, 0) and its reflection (3, 0) in the axis of symmetry.

EXAMPLE 3 Graph a function of the form y = ax 2 + bx + c STEP 6 Draw a parabola through the plotted points.

GUIDED PRACTICE for Example 3 Graph the function. Label the vertex and axis of symmetry. 4. y = x 2 – 2x – 1 SOLUTION Identify the coefficients of the function. The coefficients are a = 1, b = – 2, and c = – 1. Because a > 0, the parabola opens up. STEP 1 STEP 2 Find the vertex. Calculate the x - coordinate. Then find the y - coordinate of the vertex. (– 2) 2(1) = = 1 x = b2a b2a – y = 1 2 – = – 2

GUIDED PRACTICE for Example 3 So, the vertex is (1, – 2). Plot this point. STEP 3Draw the axis of symmetry x = 1.

GUIDED PRACTICE for Example 3 5. y = 2x 2 + 6x + 3 SOLUTION Identify the coefficients of the function. The coefficients are a = 2, b = 6, and c = 3. Because a > 0, the parabola opens up. STEP 1 STEP 2 Find the vertex. Calculate the x - coordinate. x = b2a b2a – = – = 3 2 – Then find the y - coordinate of the vertex. y = – ( ) + 6 – ( ) + 3 = – 9 So, the vertex is, – 9. Plot this point. 3 2 –

GUIDED PRACTICE for Example 3 STEP 3 Draw the axis of symmetry x = 3 2 –

GUIDED PRACTICE for Example 3 6. f (x) = x 2 – 5x – SOLUTION STEP 1 STEP 2 Find the vertex. Calculate the x - coordinate. coefficients are a =, b = – 5, and c = – Because a > 0, the parabola opens up. Identify the coefficients of the function. The x = b2a b2a – = 15 2 = ( – 5) 3 2 – ( ) 2 Then find the y - coordinate of the vertex.

GUIDED PRACTICE for Example 3 y = 3 2 – ( ) 15 2 – 5 ( ) = – 76 2 So, the vertex is,. Plot this point – 76 2 STEP 3 Draw the axis of symmetry x = 15 2