Quadratic Functions
You're viewing free preview questions — 4 questions previewing here — subscribe to unlock 130 more, plus the Full Question Bank, Mock Papers & Worksheets.Upgrade

Quadratic Functions — Free MYP5 Mathematics (Extended) Practice Questions

1QuestionMax/min valuesConcept Practice
3 marks~5 minCriterion A
A sports analyst models the height of a basketball shot using the quadratic function f(x)=a(x−h)2+kf(x) = a(x - h)^2 + k, where xx is the horizontal distance (metres) from the player and f(x)f(x) is the height (metres) of the ball.

The graph shows the ball's path. The vertex is at (0,6)(0, 6) and the parabola passes through the point (2,2.5)(2, 2.5).
a
State the values of hh and kk. [1]
b
Calculate the value of aa. [1]
c
The analyst claims the ball was released from a height greater than 5 m and that its height decreases on both sides of the launch point. Justify whether this claim is correct, using your values of aa, hh, and kk. [1]
Question diagram

Solutions

2QuestionStandard formAssessment Practice
4 marks~6 minCriterion C
A road engineer models the cross-section of a speed bump using the function f(x)=2x2−8x+6f(x) = 2x^2 - 8x + 6, where xx is the horizontal distance in metres from a reference point and f(x)f(x) is the height in metres. The graph of f(x)f(x) is provided.
a
State the coordinates of the yy-intercept of f(x)f(x). [1]
b
Find the xx-intercepts of f(x)f(x) by solving f(x)=0f(x) = 0. [1]
c
A colleague proposes the alternative model g(x)=x2−4x+3g(x) = x^2 - 4x + 3. Justify whether f(x)f(x) or g(x)g(x) produces the steeper speed-bump profile, and advise the engineer which model to select if road safety regulations require the steepest possible cross-section. [2]
Question diagram

Solutions

3QuestionVertex formAssessment Practice
8 marks~12 minCriterion D

Data

Time (tt in seconds): 0, 1, 2, 3, 4

Height (h(t)h(t) in metres): 5, 25, 35, 35, 25

The flight path is modelled as a parabola.
A drone's GPS logger records the following flight
a
Construct the quadratic function in vertex form h(t)=a(t−p)2+qh(t) = a(t - p)^2 + q that models this data. [2]
b
A height restriction of 40 metres applies in this flight zone. Deduce, using your model, whether the drone complies with this restriction. [2]
c
The model assumes a perfect parabolic path with no wind or air resistance. Advise the drone operator whether the model's compliance conclusion from part (b) alone is sufficient to authorise the flight, justifying your answer with reference to the model's limitations. [4]
Question diagram

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

Questions 5-134

Unlock these questions with Premium

Sign Up →

That's every free question here — 4 of 134.

+130 more questions, plus Mock Papers & Worksheets, are waiting in Premium.

Upgrade