Q3. - Algebra 1

Question

Consider $\mathit{y}\mathbf{=}{\mathit{x}}^{\mathbf{2}}\mathbf{-}\mathbf{7}\mathit{x}\mathbf{+}\mathbf{6}$. Determine whether the function has a maximum or minimum value.

Step-by-Step Solution

Answer

The function $y=x^2-7x+6$ has a minimum value.

Step 1. Define the concept.

In a quadratic equation $y=a{x}^2+bx+c$, if the coefficient of $x^2$ is positive, then the graph of the parabola is upward open and vertex is at the minimum and if the coefficient of width="17" style="max-width: none; vertical-align: -4px;" $x^2$is negative, then the graph of the parabola is downward open and vertex is at maximum.

Step 2. Graphical representation of the quadratic function.

The graph of any quadratic function is a parabola.

$y=a{x}^2+bx+c$ (a is positive) – minimum 

$y=a{x}^2+bx+c$ (a is negative) – maximum 

Step 3. State whether the function has a maximum or minimum value.

The function $y=x^2-7x+6$, the coefficient of $x^2$ is positive; it is upward open, so it has a minimum value.

Therefore, the function $y=x^2-7x+6$ has a minimum value.