Finding the Quadratic Equation Given the Solution Set

If you are given a solution set and need to find the quadratic equation, you can utilize the principle that when x=a and x=b are solutions, the equation can be written as (x-a)(x-b)=0. Upon expanding this, you will get the standard form of the quadratic equation, ax^2 + bx + c = 0.

The problems about Finding the Quadratic Equation Given the Solution Set

Topic	Problem	Solution
None	Write a quadratic function $f$ whose zeros are 7 …	Let's write a quadratic function $f$ whose zeros are 7 and -2.
None	Write the quadratic equation whose roots are 2 an…	Given the roots of the quadratic equation are 2 and -3, and the leading coefficient is 2.
None	determine the equation of a quadratic function wi…	The general form of a quadratic function is $f (x) = a (x - h) (x - k)$ , where h and k are the zeros of …
None	A toy rocket is launched from a 4.2 $m$ …	Given the equation for the height of the rocket as $h = - 4.9 t^{2} + 28.7 t + 4.2$ , we need to find the…
None	Find the equation of the parabola $f(x)=a x^{2}+b…	Plug in the given points into the equation to create a system of linear equations:
None	Determine the equation of a quadratic relation in…	Given the vertex form of a quadratic relation: $y = a (x - h)^{2} + k$ , where $(h, k)$ is the vert…
None	1. Use the given information to determine the equ…	Use the given information to determine the equation of each quadratic relation in vertex form, $y=a…
None	springfieldpublicschools.instructure.com Question…	Plug the value $x = - i \sqrt{5}$ into each equation and see if it satisfies the equation.
None	1. Find the equation ( in factored form) of the q…	Given x-intercepts: x1 = -2, x2 = 4 and y-intercept: y = -5
None	Write a quadratic function $f$ whose aares ar…	f(x) = a(x - r_1)(x - r_2)