Properties of Quadratic Functions

Front

What are the roots of a quadratic function?

Back

The roots of a quadratic function are the values of x for which the function equals zero. They can be found by factoring, using the quadratic formula, or graphically as the x-intercepts of the parabola.

Front

What is the shape of the graph of a quadratic function called?

Back

The graph of a quadratic function is called a parabola.

Front

How can you determine the solutions of a quadratic function from its graph?

Back

The solutions of a quadratic function can be determined by identifying the x-intercepts of the graph, where the graph crosses the x-axis.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept of a quadratic function is the point where the graph crosses the y-axis, which occurs when x = 0.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the coefficient 'a' in a quadratic function determine?

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola.

Front

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

Back

The vertex can be found using the formula x = -b/(2a) to find the x-coordinate, and then substituting this value back into the function to find the y-coordinate.

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, and it passes through the vertex.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.