Graphing Quadratics

Front

What is the y-intercept of a parabola?

Back

The y-intercept is the point where the parabola crosses the y-axis, represented as (0, y).

Front

How does the graph of g(x) = x² + 4 compare to the parent function f(x) = x²?

Back

g(x) is shifted up by 4 units.

Front

What is the standard form of a quadratic equation?

Back

The standard form is y = ax² + bx + c.

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 equation to find y.

Front

What does it mean if a parabola opens upwards?

Back

If a parabola opens upwards, it has a minimum point (the vertex) and the coefficient 'a' in y = ax² + bx + c is positive.

Front

What does it mean if a parabola opens downwards?

Back

If a parabola opens downwards, it has a maximum point (the vertex) and the coefficient 'a' in y = ax² + bx + c is negative.

Front

What is the vertex of the function f(x) = -3x² + 12x?

Back

The vertex is (2, 12).

Front

What is the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value is the y-coordinate of the vertex of the parabola.

Front

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

Back

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

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that passes through the vertex, given by x = -b/(2a).