Graphing Quadratics Review

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. It can be found using the formula x = -b/(2a) from the standard form of the quadratic equation y = ax^2 + bx + c.

Front

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

Back

In vertex form, y = a(x-h)^2 + k, the vertex is the point (h, k).

Front

What does the 'a' value in a quadratic function indicate about the graph?

Back

The 'a' value determines the direction of the parabola. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What are the roots of a quadratic function?

Back

The roots (or zeros) of a quadratic function are the x-values where the graph intersects the x-axis, which can be found by solving the equation f(x) = 0.

Front

How do you determine the range of a quadratic function?

Back

The range of a quadratic function can be determined by finding the vertex. If the parabola opens upwards, the range is [k, ∞) where k is the y-coordinate of the vertex. If it opens downwards, the range is (-∞, k].

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax^2 + bx + c, where a, b, and c are constants.

Front

How can you identify the direction a parabola opens by looking at its equation?

Back

You can identify the direction by examining the 'a' coefficient in the standard form. If 'a' > 0, it opens upwards; if 'a' < 0, it opens downwards.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on whether it opens upwards or downwards.

Front

What are x-intercepts in the context of a quadratic function?

Back

X-intercepts are the points where the graph of the quadratic function crosses the x-axis, corresponding to the roots of the equation.

Front

How do you find the x-intercepts of a quadratic function?

Back

To find the x-intercepts, set the quadratic equation equal to zero and solve for x.