Algebra Examples

$Y = X^{2}$

The minimum of a quadratic function occurs at $x = - \frac{b}{2 a}$ . If $a$ is positive, the minimum value of the function is $f (- \frac{b}{2 a})$ .

$f_{min}$ $X = a X^{2} + b X + c$ occurs at $X = - \frac{b}{2 a}$

Find the value of $X = - \frac{b}{2 a}$ .

Tap for more steps...

Substitute in the values of $a$ and $b$ .

$X = - \frac{0}{2 (1)}$

Remove parentheses.

$X = - \frac{0}{2 (1)}$

Simplify $- \frac{0}{2 (1)}$ .

Tap for more steps...

Cancel the common factor of $0$ and $2$ .

Tap for more steps...

Factor $2$ out of $0$ .

$X = - \frac{2 (0)}{2 (1)}$

Cancel the common factors.

Tap for more steps...

Cancel the common factor.

$X = - \frac{2 \cdot 0}{2 \cdot 1}$

Rewrite the expression.

$X = - \frac{0}{1}$

Divide $0$ by $1$ .

$X = - 0$

Multiply $- 1$ by $0$ .

$X = 0$

Evaluate $f (0)$ .

Tap for more steps...

Replace the variable $X$ with $0$ in the expression.

$f (0) = {(0)}^{2}$

Simplify the result.

Tap for more steps...

Raising $0$ to any positive power yields $0$ .

$f (0) = 0$

The final answer is $0$ .

$0$

Use the $x$ and $y$ values to find where the minimum occurs.

$(0, 0)$