AAC #2 Modeling Quadratics and Inequalities

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 does the vertex of a parabola represent in a quadratic function?

Back

The vertex of a parabola represents the maximum or minimum point of the quadratic function, depending on the direction of the parabola.

Front

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

Back

To find the x-intercepts, set the quadratic equation equal to zero and solve for x.

Front

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

Back

The discriminant (b² - 4ac) determines 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 standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.

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.

Front

How do you determine the direction of a parabola?

Back

The direction of a parabola opens upwards if the coefficient 'a' is positive and downwards if 'a' is negative.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).

Front

What does it mean to solve a quadratic inequality?

Back

Solving a quadratic inequality involves finding the range of values for x that satisfy the inequality, often represented on a number line.

Front

What is the process for graphing a quadratic function?

Back

To graph a quadratic function, find the vertex, axis of symmetry, x-intercepts, and y-intercept, then plot these points and draw the parabola.