Question

Identify the values of \(a, b,\) and \(c\) for the quadratic function in standard form \(y=-5 x^{2}+7 x-4\)

Short answer

For the quadratic function \(y=-5 x^{2}+7 x-4\), the values of \(a, b,\) and \(c\) are -5, 7, and -4 respectively.

Step-by-step solution

Identify the Coefficient of \(x^{2}\)

The coefficient of \(x^{2}\) in the quadratic function \(y=-5 x^{2}+7 x-4\) is -5. This is the value of \(a\), the first variable in the standard form \(y = ax^{2} + bx + c\). So, \(a = -5\).

Identify the Coefficient of \(x\)

The coefficient of \(x\) in the quadratic function \(y=-5 x^{2}+7 x-4\) is 7. This is the value of \(b\), the second variable in the standard form \(y = ax^{2} + bx + c\). Hence, \(b = 7\).

Identify the Constant Term

The constant term in the quadratic function \(y=-5 x^{2}+7 x-4\) is -4. This corresponds to \(c\), the third variable in the standard form \(y = ax^{2} + bx + c\). Thus, \(c = -4\).