# How do you find the maximum or minimum of a quadratic function?

## How do you find the maximum or minimum of a quadratic function?

Finding max/min: There are two ways to find the absolute maximum/minimum value for f(x) = ax2 + bx + c: Put the quadratic in standard form f(x) = a(x − h)2 + k, and the absolute maximum/minimum value is k and it occurs at x = h. If a > 0, then the parabola opens up, and it is a minimum functional value of f.

## What does it mean when a vertex is maximum?

i>When the parabola opens down, the vertex is the highest point on the graph — called the maximum, or max.\r\n\r\nOnly vertical parabolas can have minimum or maximum values, because horizontal parabolas have no limit on how high or how low they can go.

How do you know if the vertex is maximum or minimum?

Because the vertex can be seen in the standard form of the quadratic function, this form is also known as the vertex form of a quadratic function. As with the general form, if a>0, the parabola opens upward and the vertex is a minimum. If a<0, the parabola opens downward, and the vertex is a maximum.

Is the vertex a maximum or minimum?

If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function. If the parabola opens down, the vertex represents the highest point on the graph, or the maximum value. In either case, the vertex is a turning point on the graph.

### How do you know if its maximum or minimum?

Determine whether the function will have a minimum or a maximum depending on the coefficient of the x^2 term. If the x^2 coefficient is positive, the function has a minimum. If it is negative, the function has a maximum.

### What is the maximum of a quadratic function?

If your equation is in the form ax2 + bx + c, you can find the maximum by using the equation: max = c – (b2 / 4a).

How do you find the minimum or maximum of a vertex?

You just need to check the “a” value of the function. If a>0, then the parabola opens upward (smiley), and the y-value of the vertex is the minimum value of the function. If a<0, then the parabola opens downward (frowny), and the y-value of the vertex is the maximum value of the function.

Is the vertex a minimum or maximum?

## How do you find the maximum value of a quadratic equation?

If you are given the formula y = ax2 + bx + c, then you can find the maximum value using the formula max = c – (b2 / 4a).

## How do you find a minimum or maximum?

When a function’s slope is zero at x, and the second derivative at x is: less than 0, it is a local maximum. greater than 0, it is a local minimum.