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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. The base of the arch is located at the points (0,0) and (15,0). The maximum height of the arch is 18m. 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

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.