Solve h(t)=-98t^2+196t

$$h ( t ) = - 98 t ^ { 2 } + 196 t$$

Factor

$$98t\left(2-t\right)$$

Solution Steps

Factor out 98.

$$98\left(-t^{2}+2t\right)$$

Consider -t^{2}+2t. Factor out t.

$$t\left(-t+2\right)$$

Rewrite the complete factored expression.

$$98t\left(-t+2\right)$$

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.

$$-98t^{2}+196t=0$$

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.

$$t=\frac{-196±\sqrt{196^{2}}}{2\left(-98\right)}$$

Take the square root of 196^{2}.

$$t=\frac{-196±196}{2\left(-98\right)}$$

Multiply 2 times -98.

$$t=\frac{-196±196}{-196}$$

Now solve the equation t=\frac{-196±196}{-196} when ± is plus. Add -196 to 196.

$$t=\frac{0}{-196}$$

Divide 0 by -196.

$$t=0$$

Now solve the equation t=\frac{-196±196}{-196} when ± is minus. Subtract 196 from -196.

$$t=-\frac{392}{-196}$$

Divide -392 by -196.

$$t=2$$

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 2 for x_{2}.

$$-98t^{2}+196t=-98t\left(t-2\right)$$

Evaluate

$$98t\left(2-t\right)$$