How do you solve #y=-x^2+2x-3# and y=x-5?

Answer 1

(-1, - 6)
(2, - 3)

#y = - x^2 + 2x -3# ------------------(1)
This is a downward facing U shaped curve
y = x - 5 -------------------------(2)
Straight line cuts it at two points.

Substitute #y = - x^2 + 2x -3# in equation (2)

#- x^2 + 2x -3 = x - 5#
#- x^2 + 2x -3 - x + 5 = 0#
#- x^2 + x + 2 = 0#
#- x^2 + 2x - x + 2 = 0#
x ( - x + 2) + 1 (- x +2) = 0
(x + 1) ( - x + 2) = 0
(x + 1 = 0
x = -1

  • x + 2 = 0
    x = 2
    Substitute the x values in equation (1)
    At x = - 1 ; y = -1 - 5 = - 6

    (- 1, -6) one point

    At x = 2 ; y = 2 - 5 = 3

    (2, -3) is another point

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To solve the system of equations (y = -x^2 + 2x - 3) and (y = x - 5), set the equations equal to each other:

[ -x^2 + 2x - 3 = x - 5 ]

Rearrange the equation to set it equal to zero:

[ -x^2 + 2x - 3 - x + 5 = 0 ]

[ -x^2 + x - 2 = 0 ]

Now, solve the quadratic equation using factoring, completing the square, or the quadratic formula. Let's use factoring:

[ -(x^2 - x + 2) = 0 ]

[ -(x - 2)(x + 1) = 0 ]

Setting each factor equal to zero:

[ x - 2 = 0 ] or [ x + 1 = 0 ]

Solving for (x):

[ x = 2 ] or [ x = -1 ]

Now, substitute the values of (x) into one of the original equations to find the corresponding (y) values. Let's use (y = -x^2 + 2x - 3):

When (x = 2):

[ y = -(2)^2 + 2(2) - 3 = -4 + 4 - 3 = -3 ]

When (x = -1):

[ y = -(-1)^2 + 2(-1) - 3 = -1 - 2 - 3 = -6 ]

So, the solutions to the system of equations are the points ((2, -3)) and ((-1, -6)).

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7