Algebra 1 STAAR Category 4 Quadratics

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola. It can be found using the formula x = -b/(2a).

Front

How do you find the axis of symmetry for a quadratic function?

Back

The axis of symmetry for a quadratic function in standard form is given by the line x = -b/(2a).

Front

What is the formula for the quadratic formula?

Back

The quadratic formula is used to find the roots of a quadratic equation and is given by x = (-b ± √(b^2 - 4ac)) / (2a).

Front

What does the discriminant tell you about a quadratic equation?

Back

The discriminant, given by b^2 - 4ac, indicates the nature of the roots: if it's positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

What is the factored form of a quadratic equation?

Back

The factored form of a quadratic equation is written as f(x) = a(x - r1)(x - r2), where r1 and r2 are the roots of the equation.

Front

How do you determine the range of a quadratic function?

Back

The range of a quadratic function can be determined by finding the vertex and considering the direction of the parabola: if it opens upwards, the range is [k, ∞); if downwards, (-∞, k], where (h, k) is the vertex.

Front

What is the vertex form of a quadratic function?

Back

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

Front

How do you complete the square for a quadratic expression?

Back

To complete the square, rewrite the quadratic expression in the form (x + p)^2 - q, by adding and subtracting (b/2)^2 inside the expression.