Graphs 4
3 marks · HardA quadratic graph has the general form .
Explain how the values of , , and affect the shape and position of the graph in the coordinate plane.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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Must show: Effect of a on opening and width, Effect of b on horizontal position or symmetry, Effect of c on vertical position
Common mistakes: Confusing c with x-intercept; Not describing width or direction
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Marking points
B1 (a) · 1 mark · Describes clearly that a controls whether the parabola is U-shaped (a > 0) or inverted (a < 0), and the width (larger |a| = narrower).
B2 (a) · 1 mark · Explains that b affects the axis of symmetry or position of the vertex horizontally.
B3 (a) · 1 mark · States that c is the y-intercept (where graph crosses the y-axis).
Worked solution
The coefficient controls the direction and width of the parabola; if , the graph is U-shaped and opens upwards; if , it opens downwards. The greater the absolute value of , the narrower the graph.
The value of moves the axis of symmetry of the graph horizontally and affects the horizontal location of the vertex.
The value of is the y-intercept, the point where the graph meets the y-axis.