Math 2 Unit 3 review

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

What is a parabola?

Back

A parabola is the graph of a quadratic function, which is a U-shaped curve that can open upwards or downwards.

Front

How do you find the vertex of a parabola given in vertex form?

Back

The vertex of a parabola in vertex form y = a(x-h)^2 + k is the point (h, k).

Front

What does the 'a' value in the quadratic equation y = ax^2 + bx + c determine?

Back

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

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept of a quadratic function is the point where the graph intersects the y-axis, found by evaluating the function at x = 0.

Front

How do you determine the axis of symmetry for a parabola?

Back

The axis of symmetry for a parabola given by the equation y = ax^2 + bx + c is x = -b/(2a).

Front

What transformation occurs when a quadratic function is written in the form g(x) = (x-h)^2 + k?

Back

The transformation represents a horizontal shift to the right by h units and a vertical shift up by k units.

Front

What is the effect of adding a constant to a quadratic function?

Back

Adding a constant to a quadratic function shifts the graph vertically. If the constant is positive, the graph shifts up; if negative, it shifts down.

Front

How can you identify the direction a parabola opens from its equation?

Back

If the coefficient 'a' in the quadratic equation y = ax^2 + bx + c is positive, the parabola opens upwards; if negative, it opens downwards.

Front

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

Back

The vertex is the highest or lowest point of the parabola, depending on the direction it opens, and it represents the maximum or minimum value of the function.