b It is given that \( y=\frac{3 x^{2}-12}{5} \) For values of \( x \) in the range \( -3 \leq x \leq 2 \), find i the largest value of \( y \),

To find the largest value of \( y \) for the given range of \( x \), we need to substitute the values of \( x \) into the equation \( y=\frac{3x^{2}-12}{5} \) and determine the maximum value of \( y \) within the specified range. Given equation: \( y=\frac{3x^{2}-12}{5} \) Range of \( x \): \( -3 \leq x \leq 2 \) Let's substitute the values of \( x \) into the equation and find the corresponding values of \( y \) to determine the largest value of \( y \) within the given range. Evaluate the expression by following steps: - step0: Evaluate: \(\frac{\left(3x^{2}-12\right)}{5}\) - step1: Substitute: \(\frac{\left(3\left(-3\right)^{2}-12\right)}{5}\) - step2: Multiply the terms: \(\frac{\left(3^{3}-12\right)}{5}\) - step3: Subtract the numbers: \(\frac{15}{5}\) - step4: Divide the terms: \(3\) Substitute \( x=2 \) into the expression \( (3*x^2-12)/5 \). Evaluate the expression by following steps: - step0: Evaluate: \(\frac{\left(3x^{2}-12\right)}{5}\) - step1: Substitute: \(\frac{\left(3\times 2^{2}-12\right)}{5}\) - step2: Multiply the terms: \(\frac{\left(12-12\right)}{5}\) - step3: Subtract the terms: \(\frac{0}{5}\) - step4: Divide the terms: \(0\) Substitute \( x = -3 \) into the equation \( y = \frac{3x^{2}-12}{5} \): \( y = \frac{3(-3)^{2}-12}{5} = \frac{3(9)-12}{5} = \frac{27-12}{5} = \frac{15}{5} = 3 \) Substitute \( x = 2 \) into the equation \( y = \frac{3x^{2}-12}{5} \): \( y = \frac{3(2)^{2}-12}{5} = \frac{3(4)-12}{5} = \frac{12-12}{5} = \frac{0}{5} = 0 \) Therefore, the largest value of \( y \) within the range \( -3 \leq x \leq 2 \) is 3.