Chapter 8 Flashcards
(19 cards)
What is the general form of a quadratic equation?
y = ax^2 + bx + c
True or False: A parabola opens upwards if the coefficient ‘a’ is positive.
True
What is the vertex of a parabola?
The highest or lowest point of the parabola.
Fill in the blank: The axis of symmetry of a parabola is given by the equation _____.
x = -b/(2a)
How can you determine if a parabola opens downwards?
If the coefficient ‘a’ is negative.
What is the standard form of a parabola that opens upwards?
y = a(x - h)^2 + k
What do the variables ‘h’ and ‘k’ represent in the standard form of a parabola?
The coordinates of the vertex (h, k).
True or False: The parabola can be represented in both standard form and vertex form.
True
What is the significance of the ‘a’ value in the parabola equation?
It determines the width and direction of the parabola.
What is the formula to find the y-intercept of a parabola?
Set x = 0 in the equation y = ax^2 + bx + c.
How do you find the x-intercepts of a parabola?
Set y = 0 and solve for x.
What is the axis of symmetry for the parabola y = 2x^2 + 4x + 1?
x = -1
True or False: A parabola can intersect the x-axis at most twice.
True
Fill in the blank: The vertex form of a parabola is useful for determining the _____.
vertex
What is the axis of symmetry for a parabola in the form y = a(x - h)^2 + k?
x = h
True or False: Parabolas can be vertically or horizontally oriented.
True
What is the effect of increasing the absolute value of ‘a’ in the equation y = ax^2?
The parabola becomes narrower.
How can you convert the standard form of a parabola to vertex form?
By completing the square.
What does it mean for a parabola to have a maximum or minimum value?
It refers to the y-coordinate of the vertex being the highest or lowest point.
