Explanation 1) Approach: Step 1: Determine whether the parabola open up (or) downward. Step 2: Find the vertex. Step 3: Find the x -intercept( s ). Step 4: Find the y -intercept. Step 5: Plot one additional points. Step 6: Draw a smooth curve through the points found in step 2-5. 2) Calculation: Given, f ( x ) = x 2 − 6 x Step 1: Determine whether the parabola opens up (or) downward. f ( x ) x 2 − 6 x Given, the equation has the form a x 2 + b x + c , where a = 1 , b = − 6 and c = 0 Since, a > 0 the parabola opens upward, Step 2: Find the vertex. To find the x -co-ordinate of the vertex, we substitute the values of a and b into the formula x = − b 2 a x = − ( − 6 ) 2 ( 1 ) = 6 2 = 3 x = 3 The x -co-ordinate of the vertex is 3. To find the y-co-ordinate, we substitute 3 for x in the equation and solve for y . f ( x ) = x 2 − 6 x Let f ( x ) = y y = x 2 − 6 x Substitute, x = 3 for the above equation y = ( 3 ) 2 − 6 ( 3 ) = 9 − 18 = − 9 y = − 9 Thus, the vertex is the point ( 3 , − 9 ) Step 3: Find the x -intercept(s). To find the x -intercepts, we substitute 0 for f ( x ) and solve for x . y = x 2 − 6 x Substitute y = 0 in the above equation, 0 = x 2 − 6 x (i.e.) x 2 − 6 x = 0 Factorize x 2 − 6 x as x ( x − 6 ) , x ( x − 6 ) = 0 By the zero-factor property

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Chapter 4.1, Problem 50E

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Chapter 4.1, Problem 49E

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Ch. 4.1 - Find the vertex of the graph of the quadratic...Ch. 4.1 - Prob. 2SC Ch. 4.1 - Prob. 3SC Ch. 4.1 - Prob. 4SC Ch. 4.1 - Find the largest area possible if the association...Ch. 4.1 - A company that makes and sells baseball caps has...Ch. 4.1 - Fill in the blanks. A quadratic function is...Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E

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The quadratic function given in general form and the vertex, intercepts and axis of symmetry