Graphing Quadratics

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does it mean for a parabola to open upwards?

Back

A parabola opens upwards if the coefficient of x² (a) is positive, indicating that the vertex is a minimum point.

Front

What does it mean for a parabola to open downwards?

Back

A parabola opens downwards if the coefficient of x² (a) is negative, indicating that the vertex is a maximum point.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens up or down.

Front

How do you find the axis of symmetry (AoS) for a quadratic equation?

Back

The axis of symmetry can be found using the formula x = -b/2a.

Front

What is the y-intercept of a quadratic equation?

Back

The y-intercept is the point where the graph intersects the y-axis, found by plugging x = 0 into the equation.

Front

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

Back

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

Front

What is the maximum value of a quadratic function?

Back

The maximum value occurs at the vertex of a downward-opening parabola.

Front

What is the minimum value of a quadratic function?

Back

The minimum value occurs at the vertex of an upward-opening parabola.

Front

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

Back

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