The Quadratic Formula, symbolized as x = [-b ± sqrt(b^2 - 4ac)] / (2a), comes into play when determining the solutions of a quadratic equation in the form ax^2 + bx + c = 0. This formula is instrumental in computing the x-intercepts of the parabola, offering x values even when the equation cannot be factored.
| Topic | Problem | Solution |
|---|---|---|
| None | Solve by the quadratic formula. List the solution… | Given the quadratic equation \(3x^2 + x - 10 = 0\), we can identify the coefficients as \(a = 3\), … |
| None | A baseball player swings and hits a pop fly strai… | The height of the baseball in meters $t$ seconds after it is hit is given by the quadratic function… |
| None | Solve the equation using the quadratic formula. \… | Given the quadratic equation \(x^{2}+9 x+5=0\), we are to find the solutions for \(x\). |
| None | A ball is thrown from a height of 49 meters with … | We are given a ball thrown from a height of 49 meters with an initial downward velocity of 2 m/s. T… |
| None | A model rocket is launched with an initial upward… | We are given a model rocket is launched with an initial upward velocity of 204 ft/s. The rocket's h… |
| None | QUESTION 1 Quadratic Equation Choose one $\cdot 5… | Given the quadratic equation \(x^{2}+4 x-5=0\) |
| None | A model rocket is launched with an initial upward… | The problem is asking for the time $t$ when the height $h$ of the rocket is 35 meters. This is a qu… |
| None | Use the quadratic formula to solve for $x$. \[ 5 … | Given the quadratic equation \(5x^{2}+2x-2=0\), we are asked to find the solutions for \(x\). |
| None | Use the quadratic formula to solve for $x$ \[ 6 x… | Given the quadratic equation \(6x^{2} - 9x + 1 = 0\), we are asked to find the solutions for \(x\). |
| None | Use the quadratic formula to find both solutions … | Given the quadratic equation \(3x^{2}-x+4=0\), we can identify the coefficients as \(a=3\), \(b=-1\… |
| None | $x^{2}+x-1=0$ | The given equation is a quadratic equation in the form \(ax^{2}+bx+c=0\), where \(a=1\), \(b=1\), a… |
| None | Solve the equation using the quadratic formula. \… | The given equation is a quadratic equation in the form of \(ax^2 + bx + c = 0\). The quadratic form… |
| None | Find the zeros of the function. Give exact answer… | Given the quadratic equation \(x^2 + 7x - 3 = 0\), we can use the quadratic formula to find the exa… |
| None | 9 Solve the quadratic equation \( 21 x^{2}-12 x+1… | \(x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}\) |
| None | find the zeros of \( 3 x^{2}+13 x-10=0 \) | \( \Delta = b^{2} - 4 a c \) |
| None | \( 3 x^{2}+3=0 \) | \( x^{2} = -1 \) |
| None | \( 3 x^{2}-5 x+2=0 \) è | \( \text{Quadratic formula: } x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \) |