Solve f(x)=-4x^2+36x

$$f ( x ) = - 4 x ^ { 2 } + 36 x$$

Factor

$$4x\left(9-x\right)$$

Solution Steps

Factor out 4.

$$4\left(-x^{2}+9x\right)$$

Consider -x^{2}+9x. Factor out x.

$$x\left(-x+9\right)$$

Rewrite the complete factored expression.

$$4x\left(-x+9\right)$$

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.

$$-4x^{2}+36x=0$$

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.

$$x=\frac{-36±\sqrt{36^{2}}}{2\left(-4\right)}$$

Take the square root of 36^{2}.

$$x=\frac{-36±36}{2\left(-4\right)}$$

Multiply 2 times -4.

$$x=\frac{-36±36}{-8}$$

Now solve the equation x=\frac{-36±36}{-8} when ± is plus. Add -36 to 36.

$$x=\frac{0}{-8}$$

Divide 0 by -8.

$$x=0$$

Now solve the equation x=\frac{-36±36}{-8} when ± is minus. Subtract 36 from -36.

$$x=-\frac{72}{-8}$$

Divide -72 by -8.

$$x=9$$

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 9 for x_{2}.

$$-4x^{2}+36x=-4x\left(x-9\right)$$

Evaluate

$$4x\left(9-x\right)$$