Question

How to find the maximum value of a quadratic function?

Answer 1

To find the maximum value of a quadratic function, use the vertex formula by identifying the coefficients a, b, and c, calculating the x-coordinate of the vertex using x = -b/2a, and substituting it back into the quadratic equation to find the y-coordinate.

Step-by-step explanation:

To find the maximum value of a quadratic function, we can use the vertex formula which states that the x-coordinate of the vertex is given by x = -b/2a, where a and b are the coefficients of the quadratic function. The y-coordinate of the vertex gives us the maximum value of the quadratic function. Here are the steps:

1. Identify the coefficients a, b, and c of the quadratic function in the form ax^2 + bx + c.
2. Calculate the x-coordinate of the vertex using the formula x = -b/2a.
3. Substitute the x-coordinate back into the quadratic function to find the y-coordinate of the vertex and the maximum value of the function.

For example, let's consider the quadratic function f(x) = 2x^2 + 3x - 4:

1. a = 2, b = 3, c = -4
2. x = -3 / (2 * 2) = -3 / 4 = -0.75
3. f(-0.75) = 2(-0.75)^2 + 3(-0.75) - 4 = 0.375 - 2.25 - 4 = -5.875

Therefore, the maximum value of the quadratic function f(x) = 2x^2 + 3x - 4 is -5.875.

Answer 2

suppose

`y = a {x}^(2) + bx + c`
if a>0 it has min if 0>a it has max

`min \: y = (4ac - {b}^(2) ) / 4a`