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For the parabola defined by the equation y = -x^2 + 4x - 3, what is the y-interc

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Question: For the parabola defined by the equation y = -x^2 + 4x - 3, what is the y-intercept?

Options:

  1. -3
  2. 0
  3. 3
  4. 4

Correct Answer: -3

Solution: 

To find the y-intercept, set x = 0. The equation becomes y = -0^2 + 4(0) - 3 = -3.

For the parabola defined by the equation y = -x^2 + 4x - 3, what is the y-interc

Practice Questions

Q1
For the parabola defined by the equation y = -x^2 + 4x - 3, what is the y-intercept?
  1. -3
  2. 0
  3. 3
  4. 4

Questions & Step-by-Step Solutions

For the parabola defined by the equation y = -x^2 + 4x - 3, what is the y-intercept?
  • Step 1: Understand that the y-intercept is the point where the graph crosses the y-axis.
  • Step 2: Know that to find the y-intercept, we need to set x = 0 in the equation.
  • Step 3: Substitute x = 0 into the equation y = -x^2 + 4x - 3.
  • Step 4: Calculate y by replacing x with 0: y = -0^2 + 4(0) - 3.
  • Step 5: Simplify the equation: y = 0 + 0 - 3.
  • Step 6: Find that y = -3.
  • Step 7: Conclude that the y-intercept is the point (0, -3).
  • Finding the y-intercept – To find the y-intercept of a function, substitute x = 0 into the equation.
  • Understanding parabolas – Recognizing the standard form of a quadratic equation and its properties.
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