Home > AC > Chapter 11 > Lesson 11.2.2 > Problem11-93

11-93.

Use your graphing shortcuts to graph $f\left(x\right)=x^2-6x+5$.

Plot the $x$- and $y$-intercepts first. The $y$-intercept is given. To find the $x$-intercept,
substitute $0$ for $y$ and factor the quadratic. Plot the points you found.

1. What is the vertex?

The vertex is exactly halfway between the two $x$-intercepts because a parabola's line of symmetry is on the vertex.

At the vertex, the $x$-coordinate is $3$. Substitute $3$ into the equation to solve for $y$ and find the coordinates of the vertex.

Plot the point you found and sketch the parabola.

2. Describe the domain and range of this relation.

What is the domain of this graph, that is, what are the possible $x$-values?

What is the range, or possible $y$-values, of this graph?

D: all real numbers R: $y ≥ −4$