Quadratic Characteristics

Front

What do we call the highest or lowest point of a quadratic?

Back

Vertex

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, represented as (0, b) where b is the y-value.

Front

What is another name for the x-intercepts of a quadratic?

Back

Zeros

Front

The axis of symmetry line passes through which point?

Back

Vertex

Front

Find the zeros of the quadratic function: x^2 - 4 = 0.

Back

0 and 4

Front

What is the standard form of a quadratic equation?

Back

The standard form is y = ax^2 + bx + c, where a, b, and c are constants.

Front

What does the 'a' value in a quadratic equation 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 vertex form of a quadratic equation?

Back

The vertex form is y = a(x - h)^2 + k, where (h, k) is the vertex.

Front

How do you find the vertex of a quadratic in standard form?

Back

The vertex can be found using the formula x = -b/(2a) to find the x-coordinate, then substitute back to find the y-coordinate.

Front

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

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.