Exercise 58 Page 389

We want to graph the given quadratic function, find its vertex, $x\text{-}$intercepts, and $y\text{-}$intercept. Let's do those things one at a time.

Graphing

To graph the given quadratic function, we can start by making a table of values using five points.

Now, we can graph the function by plotting the points from the table. Because the graph of a quadratic function is a parabola, we will connect them with a smooth curve.

$y\text{-}$intercept

The point where a graph crosses the $y\text{-}$axis is called the $y\text{-}$intercept. Let's find it on our graph!

As we can see, the $y\text{-}$intercept of the given function is $(0,7).$

$x\text{-}$intercept

The points where a graph crosses the $x\text{-}$axis are called the $x\text{-}$intercepts. Let's find them on our graph!

As we can see, the $x\text{-}$intercepts of the given function are $(1,0)$ and $(7,0).$

Vertex

Because a parabola either opens upward or downward, there is always one point that is the absolute maximum or absolute minimum of the function. This point is called the vertex. Since the parabola of the given function opens upward, the vertex is be the lowest point of the graph. Let's find it!

As we can see, the vertex of the given function is $(4,\text{-}9).$