Alg. 2 Ch. 4 Test (Final) Factoring Quadratics/Transformations

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What are the zeros of a quadratic function?

Back

The zeros of a quadratic function are the values of x that make the function equal to zero. They are also known as the solutions or roots of the equation.

Front

How do you find the zeros of a quadratic equation using factoring?

Back

To find the zeros by factoring, rewrite the quadratic in the form (x - p)(x - q) = 0, where p and q are the zeros. Then, set each factor equal to zero and solve for x.

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation ax² + bx + c = 0.

Front

What does the discriminant tell you about a quadratic equation?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if > 0, there are 2 real solutions; if = 0, there is 1 real solution; if < 0, there are no real solutions.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function, found at the point (h, k) in the vertex form y = a(x - h)² + k.

Front

How do transformations affect the graph of a quadratic function?

Back

Transformations such as translations, reflections, and stretches/compressions change the position and shape of the graph of a quadratic function.

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.

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 can you determine if a quadratic opens upwards or downwards?

Back

A quadratic opens upwards if the coefficient a > 0 and downwards if a < 0.