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| Math Central | Quandaries & Queries |
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Question from Swathi, a student: A plan for an arch in the shape of a parabola is drawn on a grid with a scale of 1m per square. a)Determine the quadratic function that models that arch b)State the domain and range of the function |
Hi Swathi,
If you have a quadratic equation of the form $y = a x^2 + b x + c$ then its graph is a parabola. If you can factor the right side to obtain $y = A (x - h)(x - k)$ then $x = h$ and $x = k$ both yield $y = 0.$ Thus the graph passes through $(h, 0)$ and $(k, 0).$
The converse is also true. A quadratic (parabola) which passes through $(h, 0)$ and $(k, 0)$ has the form $y = A (x - h)(x - k).$
Form the given information you know $h = 0$ and $k = 15.$ All that remains is to find $A.$
Draw a diagram of the arch. What is the value of $x$ where the arch has its peak? Is $A$ positive or negative? What is the value of A?
Write back if you need more help,
Penny
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