The equation f(x) = x² + 2x - 3 is an illustration of a quadratic function

Calculate the left term

The equation is f(x) = x² + 2x - 3

The left term is calculated using:

[tex]x = -\frac{b}{2a}[/tex]

This gives

[tex]x = -\frac{2}{2*1}[/tex]

x = -1

Hence, the left term is -1

Compare the vertex and the axis of symmetry

The result above represents the axis of symmetry.

Substitute x = -1 in f(x) = x² + 2x - 3 to calculate the y-coordinate of the vertex

f(-1) = (-1)² + 2(-1) - 3

f(-1) = -4

This means that the vertex is (-1,-4)

So, we can conclude that the axis of symmetry passes through the x-coordinate of the vertex and it divides the graph into two equal segments.

Calculate the right term

The formula is given as:

[tex]x = \pm \frac{\sqrt{b^2 - 4ac}}{2a}[/tex]

So, we have:

[tex]x = \pm \frac{\sqrt{2^2 - 4 * 1 * -3}}{2 * 1}[/tex]

[tex]x = \pm \frac{\sqrt{16}}{2}[/tex]

Evaluate

[tex]x = \pm 2[/tex]

Hence, the right term is ±2

The horizontal distance along the axis

From the graph of the function (see attachment), we have the horizontal distance of the vertex between each x-intercept to be 2

Compare (d) and (e)

In (d), we have:

[tex]x = \pm 2[/tex]

In (e), we have:

horizontal distance = 2

This means that the horizontal distance is the absolute value of the right term.

Summary of the findings

The findings are:

- The left term represents the axis of symmetry.

- The right term represents the horizontal distance of the vertex between each x-intercept.

- The axis of symmetry divides the graph into two equal segments.

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