Graphing Quadratic Functions

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, represented as (h, k) in the vertex form y = a(x - h)² + k.

Front

How do you find the vertex of the quadratic function y = ax² + bx + c?

Back

The vertex can be found using the formula x = -b/(2a) to find the x-coordinate, then substitute back to find the y-coordinate.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating f(0).

Front

How do you find the y-intercept of the function f(x) = ax² + bx + c?

Back

Set x = 0 in the equation, resulting in f(0) = c, which gives the y-intercept (0, c).

Front

What does it mean if a quadratic function opens upwards?

Back

If a quadratic function opens upwards, the coefficient 'a' in y = ax² + bx + c is positive.

Front

What does it mean if a quadratic function opens downwards?

Back

If a quadratic function opens downwards, the coefficient 'a' in y = ax² + bx + c is negative.

Front

What is the standard form of a quadratic function?

Back

The standard form is y = ax² + bx + c, where a, b, and c are constants.

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 x = -b/(2a).

Front

How can you determine the direction a parabola opens from its equation?

Back

Look at the coefficient 'a': if 'a' > 0, it opens upwards; if 'a' < 0, it opens downwards.

Front

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

Back

The discriminant (b² - 4ac) determines the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.