Solve h(t)=-t^2+4t

$$h ( t ) = - t ^ { 2 } + 4 t$$

Factor

$$t\left(4-t\right)$$

Solution Steps

Factor out t.

$$t\left(-t+4\right)$$

Steps Using the Quadratic Formula

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$-t^{2}+4t=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$t=\frac{-4±\sqrt{4^{2}}}{2\left(-1\right)}$$

Take the square root of 4^{2}.

$$t=\frac{-4±4}{2\left(-1\right)}$$

Multiply 2 times -1.

$$t=\frac{-4±4}{-2}$$

Now solve the equation t=\frac{-4±4}{-2} when ± is plus. Add -4 to 4.

$$t=\frac{0}{-2}$$

Divide 0 by -2.

$$t=0$$

Now solve the equation t=\frac{-4±4}{-2} when ± is minus. Subtract 4 from -4.

$$t=-\frac{8}{-2}$$

Divide -8 by -2.

$$t=4$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 0 for x_{1} and 4 for x_{2}.

$$-t^{2}+4t=-t\left(t-4\right)$$

Evaluate

$$t\left(4-t\right)$$