where do y=x^2-4x-1 and y+3=-x intersect

Question

where do they intersect if they are drawn on the same set of axes.

Answer 1

Find the points of intersection by algebraically.

The quadratic equation y = x ² - 4x - 1

The linear function y + 3 = -x

 y = -x - 3 .

Substituting the expression for y  into the quadratic function, we get

x ² - 4x -1 = - x - 3

x ² - 4x - 1 + x + 3 = 0

x ² - 3x + 2  = 0

Now we solve the resulting quadratic equation for x .

 x ²  - 2x - x + 2 = 0

x( x - 2) - 1(x -2) = 0

x -2 = 0 and x -1 = 0

x = 2 and x = 1

There are two solutions to the quadratic equation: x = 2, and x  = 1.

Substituting each of these solutions into either of the two original functions (the linear one would be easier) leads us to the corresponding y  - values.

y  = - x - 3

For x = 2 then y  = -2 - 3

y  = - 5

For x = 1 then y  = -1 - 3

y  = -4

Thus, the two points of intersection are (2 , -5) and (1 , -4).

Find the points of intersection by graphically.

y = - x - 3

Compare it standard form of line y = mx + b

y = x ²- 4x - 1.

Compare it to standard form of parabola y = ax ²+ bx + c .

1. Draw coordinate plane.

2. Graph the line y = - x - 3 by using slope - intercept form.

3.Draw the parabola y = x ² - 4x -1.

From the graph the intrsection points are (1, -4) and (2,-5).