Solve -3(x-0,5)^2+9,75

$$- 3 ( x - 0,5 ) ^ { 2 } + 9,75$$

Expand

$$9+3x-3x^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-0,5\right)^{2}.

$$-3\left(x^{2}-x+0,25\right)+9,75$$

Use the distributive property to multiply -3 by x^{2}-x+0,25.

$$-3x^{2}+3x-0,75+9,75$$

Add -0,75 and 9,75 to get 9.

$$-3x^{2}+3x+9$$

Evaluate

$$-3\left(x-0,5\right)^{2}+9,75$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-0,5\right)^{2}.

$$-3\left(x^{2}-x+0,25\right)+9,75$$

Use the distributive property to multiply -3 by x^{2}-x+0,25.

$$-3x^{2}+3x-0,75+9,75$$

Add -0,75 and 9,75 to get 9.

$$-3x^{2}+3x+9$$