What is the graph of the function $$y=\text{sqrt}{x}$$ ?

The graph of the function $$y=\text{sqrt}{x}$$ is a curve that starts at the origin (0,0) and rises to the right, representing the positive square root of x.

What is the parent function of $$y = |x|$$ ?

The parent function of $$y = |x|$$ is the absolute value function, which outputs the non-negative value of x.

What is the family of functions for the equation $$y = x^2$$ ?

The family of functions for the equation $$y = x^2$$ is the quadratic functions.

What is the effect of stretching a function vertically by a factor of 2?

Stretching a function vertically by a factor of 2 means that all y-values of the function are multiplied by 2, making the graph steeper.

What is the solution to the equation $$x^2 - 4 = 0$$ ?

The solutions to the equation $$x^2 - 4 = 0$$ are $$x = 2$$ and $$x = -2$$ .

What is the vertex form of a quadratic function?

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

What does it mean for a function to have infinitely many solutions?

A function has infinitely many solutions when the equations represent the same line or curve, meaning every point on the line or curve is a solution.

What is the difference between a linear function and a quadratic function?

A linear function has a degree of 1 and graphs as a straight line, while a quadratic function has a degree of 2 and graphs as a parabola.

What is the standard form of a quadratic equation?

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

How do you identify the roots of a quadratic function?

The roots of a quadratic function can be identified using the quadratic formula: $$x = \frac{{-b \text{±} \text{sqrt}{b^2 - 4ac}}}{{2a}}$$ .

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

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

Semester 1 Final Exam: Algebra 2 Flashcards

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