The equation f(x) = x² + 2x - 3 is an illustration of a quadratic function
<h3>Calculate the left term</h3>
The equation is f(x) = x² + 2x - 3
The left term is calculated using:
![x = -\frac{b}{2a}](https://tex.z-dn.net/?f=x%20%3D%20-%5Cfrac%7Bb%7D%7B2a%7D)
This gives
![x = -\frac{2}{2*1}](https://tex.z-dn.net/?f=x%20%3D%20-%5Cfrac%7B2%7D%7B2%2A1%7D)
x = -1
Hence, the left term is -1
<h3>Compare the vertex and the axis of symmetry</h3>
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.
<h3>Calculate the right term</h3>
The formula is given as:
![x = \pm \frac{\sqrt{b^2 - 4ac}}{2a}](https://tex.z-dn.net/?f=x%20%3D%20%5Cpm%20%5Cfrac%7B%5Csqrt%7Bb%5E2%20-%204ac%7D%7D%7B2a%7D)
So, we have:
![x = \pm \frac{\sqrt{2^2 - 4 * 1 * -3}}{2 * 1}](https://tex.z-dn.net/?f=x%20%3D%20%5Cpm%20%5Cfrac%7B%5Csqrt%7B2%5E2%20-%204%20%2A%201%20%2A%20-3%7D%7D%7B2%20%2A%201%7D)
![x = \pm \frac{\sqrt{16}}{2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cpm%20%5Cfrac%7B%5Csqrt%7B16%7D%7D%7B2%7D)
Evaluate
![x = \pm 2](https://tex.z-dn.net/?f=x%20%3D%20%5Cpm%202)
Hence, the right term is ±2
<h3>The horizontal distance along the axis</h3>
From the graph of the function (see attachment), we have the horizontal distance of the vertex between each x-intercept to be 2
<h3>Compare (d) and (e)</h3>
In (d), we have:
![x = \pm 2](https://tex.z-dn.net/?f=x%20%3D%20%5Cpm%202)
In (e), we have:
horizontal distance = 2
This means that the horizontal distance is the absolute value of the right term.
<h3>Summary of the findings</h3>
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:
brainly.com/question/18797214
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