Algebra II Quadratics - Regression and Attributes

Front

What are the roots of a quadratic function?

Back

The roots of a quadratic function are the values of x for which the function equals zero. They can be found using factoring, completing the square, or the quadratic formula.

Tags

CCSS.HSA-REI.B.4B

Front

What is the range of a quadratic function in vertex form?

Back

The range of a quadratic function in vertex form y = a(x - h)² + k is determined by the vertex (h, k) and the value of 'a'. If 'a' is positive, the range is [k, ∞); if 'a' is negative, the range is (-∞, k].

Tags

CCSS.HSF-IF.C.7A

Front

How do you find the vertex of a quadratic function?

Back

The vertex of a quadratic function in standard form y = ax² + bx + c can be found using the formula x = -b/(2a). Substitute this x-value back into the function to find the corresponding y-value.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry of a quadratic function is a vertical line that divides the parabola into two mirror-image halves. It can be found using the formula x = -b/(2a).

Front

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

Back

The 'a' value in a quadratic function y = ax² + bx + c determines the direction of the parabola. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Tags

CCSS.HSF-IF.C.7A

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

How can you determine if a quadratic function has real roots?

Back

You can determine if a quadratic function has real roots by calculating the discriminant (D = b² - 4ac). If D > 0, there are two real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Tags

CCSS.HSA-REI.B.4B

Front

What is the vertex form of a quadratic function?

Back

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

Front

How do you convert from standard form to vertex form?

Back

To convert from standard form y = ax² + bx + c to vertex form y = a(x - h)² + k, complete the square.

Front

What is the significance of the y-intercept in a quadratic function?

Back

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

Tags

CCSS.HSF-IF.C.7A