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Question: How do you write the quadratic function in intercept form given x intercepts \[1,4\] and point \[\le...

How do you write the quadratic function in intercept form given x intercepts 1,41,4 and point (3,2)\left( {3,2} \right)?

Explanation

Solution

In the given question, we have been given the x-intercepts of an equation and a point. We have to find the quadratic equation in intercept form from the given information. To do that, we are going to write the intercepts in monomial form, multiply them, put them in the equation, and find the values of the remaining terms.

Complete step by step answer:
The given intercepts are 1,41,4.
Expressed in monomial form, they are,
(x−1),(x−4)\left( {x - 1} \right),\left( {x - 4} \right)
Now,
y=a(x−1)(x−4)y = a\left( {x - 1} \right)\left( {x - 4} \right)
Now, putting the values of the yy and xx from the point (3,2)\left( {3,2} \right), we have,
2=a(3−1)(3−4)2 = a\left( {3 - 1} \right)\left( {3 - 4} \right)
Hence, a=−1a = - 1
So, y=−1(x−1)(x−4)y = - 1\left( {x - 1} \right)\left( {x - 4} \right)
or y=(1−x)(x−4)y = \left( {1 - x} \right)\left( {x - 4} \right)

Note:
In the given question, we had been given the x intercepts of an equation and a point. We had to find the quadratic equation in intercept form from the given information. To do that, we wrote the intercepts in monomial form, multiplied them, put them in the equation and found the values of the remaining terms. Care must be taken while multiplication.