Solve f(3/4)=3(3/4)^2-2(3/4)+7

$$f ( \frac { 3 } { 4 } ) = 3 ( \frac { 3 } { 4 } ) ^ { 2 } - 2 ( \frac { 3 } { 4 } ) + 7$$

Evaluate

$$\frac{115}{16}=7.1875$$

Solution Steps

Calculate \frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$3\times \frac{9}{16}-2\times \frac{3}{4}+7$$

Express 3\times \frac{9}{16} as a single fraction.

$$\frac{3\times 9}{16}-2\times \frac{3}{4}+7$$

Multiply 3 and 9 to get 27.

$$\frac{27}{16}-2\times \frac{3}{4}+7$$

Express 2\times \frac{3}{4} as a single fraction.

$$\frac{27}{16}-\frac{2\times 3}{4}+7$$

Multiply 2 and 3 to get 6.

$$\frac{27}{16}-\frac{6}{4}+7$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{27}{16}-\frac{3}{2}+7$$

Least common multiple of 16 and 2 is 16. Convert \frac{27}{16} and \frac{3}{2} to fractions with denominator 16.

$$\frac{27}{16}-\frac{24}{16}+7$$

Since \frac{27}{16} and \frac{24}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27-24}{16}+7$$

Subtract 24 from 27 to get 3.

$$\frac{3}{16}+7$$

Convert 7 to fraction \frac{112}{16}.

$$\frac{3}{16}+\frac{112}{16}$$

Since \frac{3}{16} and \frac{112}{16} have the same denominator, add them by adding their numerators.

$$\frac{3+112}{16}$$

Add 3 and 112 to get 115.

$$\frac{115}{16}$$

Factor

$$\frac{5 \cdot 23}{2 ^ {4}} = 7\frac{3}{16} = 7.1875$$