more quadratics Flashcards
math (25 cards)
What is the standard form of a quadratic equation?
The standard form is ax^2 + bx + c = 0.
What does ‘a’ represent in the quadratic equation ax^2 + bx + c?
‘a’ represents the coefficient of x^2.
True or False: The graph of a quadratic function is a straight line.
False.
What is the vertex form of a quadratic equation?
The vertex form is y = a(x - h)^2 + k.
Fill in the blank: The axis of symmetry of a parabola in standard form is given by x = _____
-b/(2a).
How do you find the x-intercepts of a quadratic equation?
Set the equation to zero and solve for x.
What is the discriminant in the quadratic formula?
The discriminant is b^2 - 4ac.
What does a positive discriminant indicate?
It indicates two distinct real roots.
What are the roots of the quadratic equation x^2 - 5x + 6 = 0?
The roots are x = 2 and x = 3.
True or False: The vertex of a parabola is always at the maximum point.
False.
What is the vertex of the quadratic function y = 2(x - 3)^2 + 4?
(3, 4).
If a > 0, what direction does the parabola open?
The parabola opens upwards.
What is the formula to find the vertex from standard form?
The vertex can be found using (-b/(2a), f(-b/(2a))).
How many solutions does a quadratic equation have if the discriminant is zero?
It has one real solution.
What is the vertex of the quadratic function y = -x^2 + 4x - 3?
(2, 1).
What are the y-intercepts of the function y = x^2 - 4?
(0, -4).
What is the factored form of the quadratic equation x^2 - 6x + 8?
(x - 2)(x - 4).
True or False: The vertex of a parabola is the midpoint of the x-intercepts.
True.
What is the transformation of y = x^2 to get y = (x - 1)^2 + 2?
Shifted right 1 unit and up 2 units.
What is the minimum value of the function y = 3(x + 2)^2 - 5?
-5.
How do you determine the direction of opening for the parabola given by y = -3x^2 + 2?
Since ‘a’ is negative, it opens downwards.
What does the term ‘completing the square’ refer to in solving quadratics?
It refers to rewriting the quadratic in vertex form.
If a quadratic equation has roots at x = 1 and x = -3, what is its factored form?
(x - 1)(x + 3) = 0.
What is the sum of the roots for the quadratic equation x^2 - 7x + 10 = 0?
The sum of the roots is 7.
