Quadratic Functions
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Quadratic Functions — Free MYP4 Mathematics (Extended) Practice Questions

1QuestionVertex formAssessment Practice
2 marks~3 minCriterion D
A basketball free throw is modelled by

h(t)=−5(t−1)2+4h(t) = -5(t - 1)^2 + 4

where hh is the height of the ball in metres and tt is the time in seconds after release.
a
State the vertex of the parabola and interpret its meaning in this context. [1]
b
The rim of the basket is at a height of 3.05 m. Determine the two values of tt at which the ball is at rim height, then justify which value corresponds to a successful free throw. [1]
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Solutions

2QuestionGraphing parabolasAssessment Practice
4 marks~6 minCriterion C
A sports analyst models the height of a basketball shot using the equation y=2(x−3)2−8y = 2(x - 3)^2 - 8, where xx is the horizontal distance (metres) from the player and yy is the height (metres) relative to the release point. The graph of this parabola is shown.
a
State the coordinates of the vertex of the parabola. [1]
b
Calculate the xx-intercepts of the parabola. Show your working. [2]
c
The analyst claims the ball lands on the ground at two points either side of the player. Justify whether this claim is valid, using your results from part (b) and the context. [1]
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Solutions

3QuestionAxis of symmetryAssessment Practice
6 marks~9 minCriterion A
A water fountain projects a jet of water from a nozzle at ground level. The path is modelled by h(x)=ax2+bx+ch(x) = ax^2 + bx + c, where hh is the height (m) and xx is the horizontal distance (m). The nozzle is at x=0x = 0 and the water lands at x=dx = d. The designer wants to maximise the horizontal distance dd.
a
State the axis of symmetry of h(x)=ax2+bx+ch(x) = ax^2 + bx + c and explain what it represents in this context. [2]
b
The nozzle and landing point are both at ground level. Using the axis of symmetry, deduce that the maximum horizontal distance requires −b2a=d2-\dfrac{b}{2a} = \dfrac{d}{2}. [2]
c
A wall stands at x=3x = 3 m with height 4 m. The designer proposes h(x)=−x2+6xh(x) = -x^2 + 6x. Evaluate whether this proposal should be accepted. [2]
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Solutions

4QuestionAxis of symmetryAssessment Practice
5 marks~8 minCriterion B
A skateboard ramp is modelled by y=(x−p)2+qy = (x - p)^2 + q, where xx is the horizontal distance (metres) from a reference point and yy is the height (metres). The axis of symmetry gives the horizontal position of the ramp's lowest point.
a
Calculate the axis of symmetry for each function. [1]

y=(x−(−3))2+2y = (x-(-3))^2 + 2, y=(x−(−1))2−4\quad y = (x-(-1))^2 - 4, y=(x−0)2+5\quad y = (x-0)^2 + 5, y=(x−2)2+1\quad y = (x-2)^2 + 1, y=(x−5)2−3\quad y = (x-5)^2 - 3

Axis of symmetry: ___ , ___ , ___ , ___ , ___
b
Deduce the general rule for the axis of symmetry of y=(x−p)2+qy = (x - p)^2 + q. [1]
c
A ramp is modelled by y=(x+4)2−7y = (x + 4)^2 - 7. Use your rule to determine the horizontal position of the ramp's lowest point, showing full working and verifying your answer algebraically. [2]
d
The ramp's lowest point must lie between x=−5x = -5 and x=−3x = -3 to fit safely within the skate park. Justify whether this ramp meets the safety requirement. [1]

Solutions

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