Quadratics - Standard and Vertex Form

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. For a quadratic in standard form f(x) = ax^2 + bx + c, it can be found using the formula x = -b/(2a).

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is given by y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

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 is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, found by evaluating f(0).

Front

How do you determine the number of zeros (roots) of a quadratic function?

Back

The number of zeros can be determined using the discriminant (D = b^2 - 4ac) from the quadratic formula. If D > 0, there are 2 real roots; D = 0 means 1 real root; D < 0 means no real roots.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

How do you convert from standard form to vertex form?

Back

To convert from standard form to vertex form, complete the square on the quadratic expression.

Front

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

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola (narrower if |a| > 1, wider if |a| < 1).

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 the direction it opens.

Front

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

Back

The x-intercepts can be found by setting f(x) = 0 and solving the quadratic equation using factoring, completing the square, or the quadratic formula.