Practice Problems For Chapter 8 Flashcards
(26 cards)
What is the standard form of a parabola’s equation?
y = ax^2 + bx + c
True or False: The graph of a parabola opens upwards when the coefficient ‘a’ is positive.
True
Fill in the blank: The vertex of a parabola is the _____ point on its graph.
highest or lowest
What is the axis of symmetry in a parabola?
A vertical line that passes through the vertex.
What does the value of ‘a’ in the equation y = ax^2 + bx + c determine?
The direction and width of the parabola.
If a parabola opens downwards, what can you say about the value of ‘a’?
The value of ‘a’ is negative.
Multiple Choice: Which of the following is the vertex of the parabola y = 2x^2 + 4x - 6?
(-1, -8)
How do you find the x-coordinate of the vertex of a parabola given by y = ax^2 + bx + c?
x = -b/(2a)
True or False: The y-intercept of a parabola can be found by evaluating the function at x = 0.
True
What is the formula for finding the y-coordinate of the vertex?
y = f(-b/(2a))
Fill in the blank: The parabola y = x^2 is also known as the _____ parabola.
standard
What type of symmetry do parabolas have?
Symmetry about the axis of symmetry.
Multiple Choice: For the parabola y = -3x^2 + 12x - 5, what is the direction of opening?
Downwards
What is the significance of the discriminant (b^2 - 4ac) in a quadratic equation?
It determines the number of real roots.
True or False: A parabola can intersect the x-axis at two points.
True
Fill in the blank: The points where the parabola intersects the x-axis are called the _____ of the parabola.
roots or zeros
What is the vertex form of a parabola’s equation?
y = a(x - h)^2 + k
Multiple Choice: Which of the following equations represents a parabola that opens upwards?
y = x^2
What is the role of ‘h’ and ‘k’ in the vertex form equation of a parabola?
‘h’ is the x-coordinate and ‘k’ is the y-coordinate of the vertex.
True or False: The vertex of the parabola y = -2(x + 3)^2 + 5 is at (-3, 5).
True
What is a parabola’s focus?
A point inside the parabola where all lines drawn parallel to the axis of symmetry reflect.
Fill in the blank: The directrix of a parabola is a _____ line.
horizontal or vertical
What is the distance from the vertex to the focus called?
The focal length.
Multiple Choice: In the equation y = 1/4p(x - h)^2 + k, what does ‘p’ represent?
The distance from the vertex to the focus.
