9.1 Characteristics of Quadratics

Front

What is the axis of symmetry of a quadratic graph?

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) for a quadratic in the form ax^2 + bx + c.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. It can be found at the coordinates (h, k) in the vertex form of a quadratic equation: y = a(x-h)^2 + k.

Front

Define the Y-intercept of a quadratic function.

Back

The Y-intercept is the point where the graph of the quadratic function intersects the y-axis. It occurs when x = 0.

Front

What does the term 'parabola' refer to in mathematics?

Back

A parabola is a U-shaped curve that is the graph of a quadratic function. It can open upwards or downwards.

Front

How can you determine if a quadratic opens upwards or downwards?

Back

If the coefficient 'a' in the quadratic equation y = ax^2 + bx + c is positive, the parabola opens upwards. If 'a' is negative, it opens downwards.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum value of the quadratic function, indicating the highest or lowest point on the graph.

Front

What is the formula for finding the axis of symmetry?

Back

The formula for the axis of symmetry is x = -b/(2a), where a and b are coefficients from the quadratic equation in standard form.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph intersects the x-axis, found by solving the equation ax^2 + bx + c = 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax^2 + bx + c, where a, b, and c are constants.

Front

What is the difference between the vertex form and standard form of a quadratic equation?

Back

The vertex form is y = a(x-h)^2 + k, which highlights the vertex (h, k), while the standard form is y = ax^2 + bx + c.