Characteristics of 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) = ax² + 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 y = ax² + bx + c.

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which opens upwards if a > 0 and downwards if a < 0.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

How do you find the axis of symmetry of a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a), where a and b are coefficients from the quadratic equation.

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 ax² + bx + c = 0.

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) = c.

Front

What is the minimum value of a quadratic function?

Back

The minimum value occurs at the vertex of the parabola when it opens upwards.

Front

What is the maximum value of a quadratic function?

Back

The maximum value occurs at the vertex of the parabola when it opens downwards.

Front

What is the significance of the coefficient 'a' in a quadratic function?

Back

The coefficient 'a' determines the direction of the parabola (upward or downward) and affects the width of the parabola.