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Questions and Answers
What is the equation of the axis of symmetry of the parabola $y = 2x^2 - 4x + 3$?
What is the equation of the axis of symmetry of the parabola $y = 2x^2 - 4x + 3$?
- x = -1
- x = 1
- x = 1/2
- x = 2 (correct)
If a parabola has a vertex at (2, 3) and passes through the point (4, 7), what is the equation of the parabola?
If a parabola has a vertex at (2, 3) and passes through the point (4, 7), what is the equation of the parabola?
- y = (x - 2)^2 + 1
- y = (x - 4)^2 + 7
- y = (x - 2)^2 + 2
- y = (x - 2)^2 + 3 (correct)
What is the x-coordinate of the vertex of the parabola $y = x^2 - 6x + 8$?
What is the x-coordinate of the vertex of the parabola $y = x^2 - 6x + 8$?
- 5
- 2
- 3 (correct)
- 4
If a parabola has a focus at (3, 0) and a directrix at x = -1, what is the equation of the parabola?
If a parabola has a focus at (3, 0) and a directrix at x = -1, what is the equation of the parabola?
What is the equation of the parabola that passes through the points (0, 1), (2, 3), and (4, 7)?
What is the equation of the parabola that passes through the points (0, 1), (2, 3), and (4, 7)?
Flashcards
Axis of symmetry for y = 2x^2 - 4x + 3?
Axis of symmetry for y = 2x^2 - 4x + 3?
x = 1
Parabola equation with vertex (2, 3) through (4, 7)?
Parabola equation with vertex (2, 3) through (4, 7)?
y = (x - 2)^2 + 3
x-coordinate of the vertex of y = x^2 - 6x + 8?
x-coordinate of the vertex of y = x^2 - 6x + 8?
x = 3
Parabola equation with focus (3, 0) and directrix x = -1?
Parabola equation with focus (3, 0) and directrix x = -1?
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Parabola equation through (0, 1), (2, -3), and (4, 5)?
Parabola equation through (0, 1), (2, -3), and (4, 5)?
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Study Notes
Parabola Study Notes (Grade 10, CAPS, South Africa)
What is a Parabola?
- A parabola is a type of quadratic curve in the shape of a U, which opens upwards or downwards.
Equation of a Parabola
- The standard form of a parabola's equation is y = ax^2 + bx + c, where a, b, and c are constants.
- The graph of a parabola can be identified by the coefficient of the x^2 term, which is 'a'.
Characteristics of a Parabola
- The vertex of a parabola is the turning point, where the curve changes direction.
- The axis of symmetry is the vertical line that passes through the vertex, and it divides the parabola into two identical halves.
- The y-intercept of a parabola is the point at which the curve crosses the y-axis.
Graphing a Parabola
- To graph a parabola, start by plotting the y-intercept, then use the coefficient 'a' to determine the shape of the curve.
- If 'a' is positive, the parabola opens upwards. If 'a' is negative, the parabola opens downwards.
Solving Problems Involving Parabolas
- To solve problems involving parabolas, use the equation to find the vertex, axis of symmetry, and y-intercept.
- Use the graph to identify the maximum or minimum value of the parabola, and the x-intercepts.
Tips for Exam Questions
- Read the question carefully to identify the type of parabola problem being asked.
- Use the standard form of the equation to solve the problem.
- Label the vertex, axis of symmetry, and y-intercept on the graph to ensure accuracy.
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