Parabola Equations (Period 4)

Front

What is the axis of symmetry of 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

What is the vertex of a parabola given in the form y = a(x - h)^2 + k?

Back

The vertex of the parabola is the point (h, k), where 'h' is the x-coordinate and 'k' is the y-coordinate.

Front

How do you find the zeros of a quadratic function?

Back

To find the zeros of a quadratic function f(x) = ax^2 + bx + c, set f(x) = 0 and solve for x using factoring, completing the square, or the quadratic formula.

Front

What is the standard form of a parabola?

Back

The standard form of a parabola is y = ax^2 + bx + c, where 'a' determines the direction and width of the parabola.

Front

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

Back

The 'a' value indicates the direction of the parabola: 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 its orientation. It represents the maximum or minimum value of the function.

Front

How do you determine if a parabola opens upwards or downwards?

Back

Check the value of '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 the axis of symmetry of a parabola given by the equation y = ax^2 + bx + c?

Back

The formula for the axis of symmetry is x = -b/(2a).

Front

How can you convert the vertex form of a parabola to standard form?

Back

To convert from vertex form y = a(x - h)^2 + k to standard form y = ax^2 + bx + c, expand the equation and simplify.

Front

What are the x-intercepts of a parabola?

Back

The x-intercepts are the points where the parabola crosses the x-axis, found by solving the equation f(x) = 0.