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.
Read more about quadratic functions at:
https://brainly.com/question/18797214
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