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Whenever the equation is given in a completed square form, these are what we need
1. Smiley or sad? Based on the signage of the coefficient of x^2; if positive it’s smiley; if negative it’s sad
2. Locate turning point; x-coordinate is found by setting term in brackets to 0 (here, x - 5 = 0); term outside the brackets is the y-coordinate of the turning point (here, 16)
3. Evaluate y-intercept
4. Draw the graph, by marking out the position of the y-intercept and the turning point; these two points are sufficient to draw the curve since the curve is going to turn at the turning point anyway
The x-intercepts are not required for completed square graphs, because sometimes they don’t even exist (as is the case here). Note that there is always one turning point and always one y-intercept for quadratic graphs.
1. Smiley or sad? Based on the signage of the coefficient of x^2; if positive it’s smiley; if negative it’s sad
2. Locate turning point; x-coordinate is found by setting term in brackets to 0 (here, x - 5 = 0); term outside the brackets is the y-coordinate of the turning point (here, 16)
3. Evaluate y-intercept
4. Draw the graph, by marking out the position of the y-intercept and the turning point; these two points are sufficient to draw the curve since the curve is going to turn at the turning point anyway
The x-intercepts are not required for completed square graphs, because sometimes they don’t even exist (as is the case here). Note that there is always one turning point and always one y-intercept for quadratic graphs.
Date Posted:
4 years ago