Quadratic Functions - Standard Form

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the vertex of a parabola represent?

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

Back

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

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 the function at x = 0.

Front

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

Back

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

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

Front

How can you determine if a quadratic function has a maximum or minimum value?

Back

If 'a' is positive, the function has a minimum value; if 'a' is negative, it has a maximum value.

Front

What is the formula to find the y-coordinate of the vertex?

Back

The y-coordinate of the vertex can be found by substituting x = -b/(2a) into the quadratic function.

Front

What does it mean if a quadratic function has two real roots?

Back

It means the graph intersects the x-axis at two points, indicating two distinct solutions for the equation.

Front

What does it mean if a quadratic function has one real root?

Back

It means the graph touches the x-axis at one point (the vertex), indicating a repeated solution for the equation.