Page 63 - The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007

3. Solving Problems Involving Quadratic Functions
By the end of this course, students will:
3.1 collect data that can be modelled as a quad- ratic function, through investigation with and without technology, from primary sources, using a variety of tools (e.g., concrete materi- als; measurement tools such as measuring tapes, electronic probes, motion sensors), or from secondary sources (e.g., websites such as Statistics Canada, E-STAT), and graph
the data
Sample problem: When a 3 x 3 x 3 cube made up of 1 x 1 x 1 cubes is dipped into red paint, 6 of the smaller cubes will have 1 face paint- ed. Investigate the number of smaller cubes with 1 face painted as a function of the edge length of the larger cube, and graph the function.
3.2 determine, through investigation using a vari- ety of strategies (e.g., applying properties of quadratic functions such as the x-intercepts and the vertex; using transformations), the equation of the quadratic function that best models a suitable data set graphed on a scatter plot, and compare this equation to the equation of a curve of best fit generated with technology (e.g., graphing software, graphing calculator)
3.3 solve problems arising from real-world appli- cations, given the algebraic representation of a quadratic function (e.g., given the equation of a quadratic function representing the height of a ball over elapsed time, answer questions that involve the maximum height of the ball, the length of time needed for the ball to touch the ground, and the time interval when the ball is higher than a given measurement)
Sample problem: In the following DC electri- cal circuit, the relationship between the power used by a device, P (in watts, W), the electric potential difference (voltage), V (in volts, V), the current, I (in amperes, A), and the resistance, R (in ohms, Ω ), is represented by the formula P = IV – I 2R. Represent graphically and algebraically the relationship between the power and the current when the electric potential difference is 24 V and the resistance is 1.5 Ω. Determine the current needed in order for the device to use the maximum amount of power.
R
I
Device
V
QUADRATIC FUNCTIONS
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Functions and Applications
MCF3M