Solve g(x)=-1/3(x-15)^2+50?

$$g ( x ) = - \frac { 1 } { 3 } ( x - 15 ) ^ { 2 } + 50 ?$$

Evaluate

$$-\frac{\left(x-15\right)^{2}}{3}+50$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-15\right)^{2}.

$$-\frac{1}{3}\left(x^{2}-30x+225\right)+50$$

Use the distributive property to multiply -\frac{1}{3} by x^{2}-30x+225.

$$-\frac{1}{3}x^{2}+10x-75+50$$

Add -75 and 50 to get -25.

$$-\frac{1}{3}x^{2}+10x-25$$

Expand

$$-\frac{x^{2}}{3}+10x-25$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-15\right)^{2}.

$$-\frac{1}{3}\left(x^{2}-30x+225\right)+50$$

Use the distributive property to multiply -\frac{1}{3} by x^{2}-30x+225.

$$-\frac{1}{3}x^{2}+10x-75+50$$

Add -75 and 50 to get -25.

$$-\frac{1}{3}x^{2}+10x-25$$