Algebra 2: 3rd six weeks EC

Front

What is the axis of symmetry for a parabola?

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) for a quadratic equation in the form y = ax^2 + bx + c.

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 indicate?

Back

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

Front

What is the significance of the vertex in a parabola?

Back

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

Front

How do you determine if a parabola has a maximum or minimum value?

Back

If the parabola opens upwards (a > 0), it has a minimum value at the vertex. If it opens downwards (a < 0), it has a maximum value at the vertex.

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

By examining the coefficient 'a' in the equation y = ax^2 + bx + c: if 'a' > 0, it opens upwards; if 'a' < 0, it opens downwards.

Front

What is the formula for finding the x-coordinate of the vertex of a parabola?

Back

The x-coordinate of the vertex can be found using the formula x = -b/(2a), where a and b are coefficients from the quadratic equation.

Front

What is the relationship between the roots of a quadratic equation and its graph?

Back

The roots (or x-intercepts) of a quadratic equation are the points where the graph intersects the x-axis. They can be found using factoring, completing the square, or the quadratic formula.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.