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Interpreting Quadratic Functions in Factored Form

Interpreting Quadratic Functions in Factored Form 1.14 - Solution

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

  1. Identify and plot the intercepts.
  2. Find and graph the axis of symmetry.
  3. Find and plot the vertex.
  4. Draw the parabola through the vertex and the points where the intercepts occur.

Let's go through these steps one at a time.

Identify and Plot the intercepts

Recall the factored form of a quadratic function. In this form, where the intercepts are and Let's consider the factored form of our function. We can see that and Therefore, the intercepts occur at and

Find and Graph the Axis of Symmetry

The axis of symmetry is halfway between and Since we know that and the axis of symmetry of our parabola is halfway between and We found that the axis of symmetry is the vertical line

Find and Plot the Vertex

Since the vertex lies on the axis of symmetry, its coordinate is To find the coordinate, we will substitute for in the given equation.
Simplify right-hand side
The coordinate of the vertex is Therefore, the vertex is the point

Draw the Parabola

Finally, we will draw the parabola through the vertex and the intercepts.