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Standard 8.0

(–8) 2(2). –. –. x =. = 2. =. b 2 a. Standard 8.0. Graph a function of the form y = ax 2 + bx + c. Graph y = 2 x 2 – 8 x + 6. SOLUTION. STEP 1.

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Standard 8.0

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  1. (–8) 2(2) – – x = = 2 = b 2a Standard 8.0 Graph a function of the form y = ax2 + bx + c Graph y = 2x2 – 8x + 6. SOLUTION STEP 1 Identify the coefficients of the function. The coefficients are a = 2, b = –8, and c = 6. Because a > 0, the parabola opens up. If a < 0 then the parabola open down. Find the vertex. Calculate the x-coordinate. STEP 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.

  2. Standard 8.0 Graph a function of the form y = ax2 + bx + c STEP 3 Draw the axis of symmetry x = 2. STEP 4 Identify the y-intercept c, remember that the graph intercepts the y axis when x = 0 . So we plug in x = 0 into our original equation y = 2(0)2– 8(0) + 6 = 6 Plot the point (0, 6). Then reflect this point in the axis of symmetry to plot another point, (4, 6). STEP 5 Solve the equation by any of the three methods (factoring, completing the square or using the quadratic formula). The solutions are x = 3 and x = 1 plot the points (3,0) and (1,0) on the “x”axis.

  3. EXAMPLE 1 Graph a function of the form y = ax2 + bx + c STEP 6 Draw the axis of symmetry x = 2. Plot the point (0, 6). Then reflect this point in the axis of symmetry to plot another point (4, 6). Plot the points (3,0) and (1,0) on the “x”axis.

  4. EXAMPLE 1 Graph a function of the form y = ax2 + bx + c Draw a parabola through the plotted points. STEP 6

  5. for graphing quadratic equations GUIDED PRACTICE Graph the function. Label the vertex and axis of symmetry. 5. y = 2x2 + 6x + 3 4. y = x2 – 2x – 1

  6. 6. f (x) = x2 – 5x + 2 – 1 3 for graphing quadratic equations GUIDED PRACTICE

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