Question

Select all the correct answers.

Look at the graphs of y = 4x2 + 7x - 11 and y = 3x + 4. At which points are the two equations equal?
410
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8
7
6
5
4
3
27-1
y = 3x + 4

Answer 1

Second point (-5/2, -7/2)

First point (3/2, 17/2)

Explanation:

We have two equations, and we want to know at wich poin are equal. Hence, we have a system of equations and the solution is nothing more that the point (x,y) where those functions intercepts.

4x2+ 7x -11=y

3x+4=y

Lets use substitute method

4x2+7x-11=3x+4

This can be re arrange as the following eq:

4x2+4x-15=0

A quadratic equation, its solution can be obtained using the below eq.

`x=\frac{-b+/- \sqrt{x^(2)-4ac } }{2a}`

where a=4, b=4, c=-15.

Remember, the quadratic equation as a +/- sign, meaning that you will obtain one answer using the + operator and other using the - operator.

By doing the above, we have x=-5/2 and x=3/2

By using x=3/2 in equation of line (3x+4=y) we have y=17/2

First point (3/2, 17/2)

By using x=-5/2 in equation of line (3x+4=y) we have y= -7/2

Second point (-5/2, -7/2)

Those points are the ones where the line and the parabola intercept.