0 like 0 dislike
The answer for B and C I have but I need help with D-G though please. Please help me out.
The answer for B:
x-intercepts are (1,0) and (-3,0)

The answer for C:
The axis of symmetry is the x coordinate of the midpoint of x-intercepts:(1-3)/2=-1, x=-1 is the axis of symmetry.
by

1 Answer

0 like 0 dislike
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:

 

by
Welcome to AskTheTask.com, where understudies, educators and math devotees can ask and respond to any number related inquiry. Find support and replies to any numerical statement including variable based math, geometry, calculation, analytics, geometry, divisions, settling articulation, improving on articulations from there, the sky is the limit. Find solutions to numerical problems. Help is consistently 100 percent free!

Questions

No related questions found