Quadratic Key Features

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, represented as (0, f(0)).

Front

How do you identify the vertex of a quadratic function from its graph?

Back

The vertex is the highest or lowest point on the graph of the quadratic function, depending on whether it opens upwards or downwards.

Front

What are x-intercepts in a quadratic function?

Back

X-intercepts are the points where the graph intersects the x-axis, represented as (x, 0).

Front

How do you factor a quadratic expression in the form x^2 + bx + c?

Back

To factor, find two numbers that multiply to c and add to b, then express the quadratic as (x + m)(x + n) where m and n are those numbers.

Front

What is the standard form of a quadratic function?

Back

The standard form is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

What does the 'a' value in a quadratic function determine?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).

Front

How can you find the vertex using the standard form of a quadratic function?

Back

The vertex can be found using the formula (h, k) where h = -b/(2a) and k = f(h).

Front

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

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

Front

What is the vertex form of a quadratic function?

Back

The vertex form is f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.