Quadratic Graphs

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c = 0.

Front

What is the vertex of a parabola?

Back

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

Front

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

Back

A parabola opens upwards if the coefficient 'a' in the quadratic function f(x) = ax^2 + bx + c is positive, and it opens downwards if 'a' is negative.

Front

What are the x-intercepts of a quadratic function?

Back

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

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept of a quadratic function is the point where the graph intersects the y-axis, found by evaluating the function at x = 0.

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, given by the formula x = -b/(2a).

Front

What is the formula to find the vertex of a parabola in standard form?

Back

The vertex (h, k) of a parabola in standard form y = ax^2 + bx + c can be found using h = -b/(2a) and k = f(h).

Front

What is the difference between maximum and minimum values in a quadratic function?

Back

A maximum value is the highest point of a parabola that opens downwards, while a minimum value is the lowest point of a parabola that opens upwards.

Front

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

Back

The maximum or minimum value can be found by evaluating the function at the vertex, which is given by k = f(h) where h = -b/(2a).