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Question
Write the standard form of a quadratic polynomial with real coefficients.
Solution
Any quadratic polynomial in variable x with real coefficients is of the form `f(x)=bx + c `, where `a,b,c `are real numbers and `a ≠ 0`
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Case Study -1
The figure given alongside shows the path of a diver, when she takes a jump from the diving board. Clearly it is a parabola.
Annie was standing on a diving board, 48 feet above the water level. She took a dive into the pool. Her height (in feet) above the water level at any time‘t’ in seconds is given by the polynomial h(t) such that h(t) = -16t2 + 8t + k.
At what time will she touch the water in the pool?
The below picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.
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Basketball and soccer are played with a spherical ball. Even though an athlete dribbles the ball in both sports, a basketball player uses his hands and a soccer player uses his feet. Usually, soccer is played outdoors on a large field and basketball is played indoor on a court made out of wood. The projectile (path traced) of soccer ball and basketball are in the form of parabola representing quadratic polynomial.
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If a polynomial p(x) is given by p(x) = x2 - 5x + 6, then the value of p(1) + p(4) is ______.
