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How to sketch a quadratic graph by completing the square
Step 1: Complete the square for the given quadratic graph (Please refer to video on completing the square if unsure about how to complete the square).
Step 2: Determine the x and y coordinates of the vertex (also known as the turning point which is either a maximum or minimum point).
Step 3: To know whether the turning point is maximum or minimum, check the coefficient of x2 term. If coefficient is more than 0, the turning point is minimum point and graph resembles a "smiley face" (U SHAPE). If coefficient of x2 term is less than 0, the turning point is maximum point and graph resembles a "sad face" (∩ SHAPE).
Step 4: Determine the x-intercepts (if any). To do so, let y=0 in the given quadratic equation to find the x-intercepts.
Step 5: Determine the y-intercept. To do so, let x=0 in the given quadratic equation to find y-intercept.
Step 6: Draw your x-axis and y-aixs and write down all information from above steps into your axes of the graph (your x-intercepts, y-intercept and coordinates of turning point and you are ready to sketch the quadratic graph.
*Take note that in this video, the graph is lying above the x-axis, so there is no x-intercepts to find here. But, some graphs have x-intercepts that you are required to find.
Step 2: Determine the x and y coordinates of the vertex (also known as the turning point which is either a maximum or minimum point).
Step 3: To know whether the turning point is maximum or minimum, check the coefficient of x2 term. If coefficient is more than 0, the turning point is minimum point and graph resembles a "smiley face" (U SHAPE). If coefficient of x2 term is less than 0, the turning point is maximum point and graph resembles a "sad face" (∩ SHAPE).
Step 4: Determine the x-intercepts (if any). To do so, let y=0 in the given quadratic equation to find the x-intercepts.
Step 5: Determine the y-intercept. To do so, let x=0 in the given quadratic equation to find y-intercept.
Step 6: Draw your x-axis and y-aixs and write down all information from above steps into your axes of the graph (your x-intercepts, y-intercept and coordinates of turning point and you are ready to sketch the quadratic graph.
*Take note that in this video, the graph is lying above the x-axis, so there is no x-intercepts to find here. But, some graphs have x-intercepts that you are required to find.