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Interpreting Quadratic Functions in Vertex Form

Interpreting Quadratic Functions in Vertex Form 1.16 - Solution

arrow_back Return to Interpreting Quadratic Functions in Vertex Form

To draw the graph of the given quadratic function, we will follow five steps.

  1. Identify and plot the vertex.
  2. Draw the axis of symmetry.
  3. Determine and plot the intersection with the vertical axis.
  4. Reflect the intersection with the vertical axis across the axis of symmetry.
  5. Draw the parabola.

Identify and Plot the Vertex

Note that the function is expressed in vertex form. Let's compare the general formula for the vertex form with our function. We can see that and Recall that the vertex of a quadratic function written in vertex form is the point Therefore, the vertex of the given equation is Let's plot the vertex on a coordinate plane.

Draw the Axis of Symmetry

The axis of symmetry of a quadratic function written in vertex form is the vertical line with equation As we have already noticed, for our function, this is Therefore, the axis of symmetry is the line

Determine and Plot the intercept

Recall that the first coordinate of the point where the parabola intercepts the vertical axis is Therefore, to find the its second coordinate, we will substitute in the function.
Simplify right-hand side
The intersection of the parabola and the vertical axis occurs at the point

Reflect the Intersection With the Vertical Axis Across the Axis of Symmetry

The axis of symmetry divides the parabola into two mirror images. Therefore, points on one side of the parabola can be reflected across the axis of symmetry. Notice that the intersection with the vertical axis is units away from the axis of symmetry. Thus, there exists another point directly across the axis of symmetry that is also units away, in the opposite direction.

Draw the parabola

Now, with three points plotted, the general shape of the parabola can be seen. It appears that the parabola faces upward. Since in the given function rule, this should be expected. To draw the parabola, we will connect the points with a smooth curve. Note that negative values for do not make sense. We will draw the curve for