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.
| 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 $\mathrm{m}$ … | 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) |