Quadratic Properties 2

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the point where the parabola changes direction. It is the highest or lowest point of the graph, depending on whether it opens upwards or downwards.

Front

How do you find the axis of symmetry of a parabola?

Back

The axis of symmetry of a parabola can be found using the formula x = -b/(2a) from the quadratic equation in the form y = ax^2 + bx + c.

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 and a ≠ 0.

Front

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

Back

The 'a' value in a quadratic equation 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 y-intercept of a quadratic function?

Back

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

Front

How can you determine if a quadratic function has a maximum or minimum value?

Back

A quadratic function has a maximum value if it opens downwards (a < 0) and a minimum value if it opens upwards (a > 0).

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (D = b^2 - 4ac) determines the nature of the roots of a quadratic equation. If D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

What is the formula for the vertex of a parabola given in standard form?

Back

The vertex (h, k) of a parabola in standard form y = a(x - h)^2 + k can be found directly from the equation, where (h, k) is the vertex.

Front

What is the relationship between the vertex and the axis of symmetry?

Back

The axis of symmetry of a parabola passes through the vertex, dividing the parabola into two mirror-image halves.

Front

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

Back

The x-intercepts of a quadratic function can be found by setting the function equal to zero and solving for x, often using the quadratic formula x = (-b ± √D) / (2a).