Graphing Quadratics

Front

What is a parabola?

Back

A parabola is a U-shaped curve that represents the graph of a quadratic function. It can open upwards or downwards depending on the coefficient of the squared term.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the coefficient 'a' in a quadratic equation indicate about the parabola?

Back

The coefficient 'a' determines the direction of the parabola's opening: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its direction. It can be found using the formula (-b/2a, f(-b/2a)).

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. It can be found using the formula x = -b/2a.

Front

How do you find the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex of the parabola. For a downward-opening parabola, it's the y-coordinate of the vertex (maximum); for an upward-opening parabola, it's the y-coordinate of the vertex (minimum).

Front

What is the range of a parabola that opens upwards?

Back

The range of an upward-opening parabola is [k, ∞), where k is the y-coordinate of the vertex.

Front

What is the range of a parabola that opens downwards?

Back

The range of a downward-opening parabola is (-∞, k], where k is the y-coordinate of the vertex.

Front

How do you determine the y-intercept of a quadratic function?

Back

The y-intercept can be found by evaluating the function at x = 0, which gives the point (0, c) in the standard form y = ax² + bx + c.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if it's positive, there are two real roots; if zero, one real root; if negative, no real roots.