Quadratics Graphing Review

Front

What is the vertex of a quadratic equation?

Back

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

Front

How can you determine the direction in which a quadratic graph opens?

Back

The direction of the graph is determined by the coefficient 'a' in the quadratic equation y = ax² + bx + c. If 'a' is positive, the graph opens upwards; if 'a' is negative, it opens downwards.

Front

What is the minimum or maximum value of a quadratic function?

Back

The minimum or maximum value is the y-coordinate of the vertex. It is the highest point (maximum) if the graph opens downwards and the lowest point (minimum) if it opens upwards.

Front

What does it mean if a quadratic graph has a minimum?

Back

A quadratic graph has a minimum if it opens upwards, indicating that the vertex represents the lowest point on the graph.

Front

What does it mean if a quadratic graph has a maximum?

Back

A quadratic graph has a maximum if it opens downwards, indicating that the vertex represents the highest point on the graph.

Front

How do you find the vertex of a quadratic equation in standard form?

Back

To find the vertex of a quadratic equation in standard form y = ax² + bx + c, use the formula h = -b/(2a) and k = f(h) to find the coordinates (h, k).

Front

What is the axis of symmetry in a quadratic graph?

Back

The axis of symmetry is a vertical line that divides the graph into two mirror-image halves, given by the equation x = h, where h is the x-coordinate of the vertex.

Front

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

Back

The discriminant (D = b² - 4ac) determines the nature of the roots of the quadratic equation. If D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

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 is the vertex form of a quadratic equation?

Back

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