Semester 1 Review_Alg2_24-25

Front

What is the equation of a circle with center (h, k) and radius r?

Back

The equation is given by: $$(x - h)^2 + (y - k)^2 = r^2$$.

Front

How do you determine if a point (x, y) is inside, outside, or on a circle defined by the equation $$x^2 + y^2 = r^2$$?

Back

Calculate $$d^2 = x^2 + y^2$$. If $$d^2 < r^2$$, the point is inside; if $$d^2 = r^2$$, it is on the circle; if $$d^2 > r^2$$, it is outside.

Front

What is the vertex form of a quadratic function?

Back

The vertex form is given by: $$f(x) = a(x - h)^2 + k$$, where (h, k) is the vertex of the parabola.

Front

How do you convert a quadratic function from standard form to vertex form?

Back

Use completing the square method to rewrite the function in the form $$f(x) = a(x - h)^2 + k$$.

Front

What is the domain of a function?

Back

The domain is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range is the set of all possible output values (y-values) that the function can produce.

Front

How do you find the domain of a quadratic function?

Back

For a quadratic function, the domain is all real numbers, expressed as $$(- ext{∞}, ext{∞})$$.

Front

What is an exponential function?

Back

An exponential function is of the form $$y = ab^x$$, where a is a constant, b is the base, and x is the exponent.

Front

How do you find the equation of an exponential function given two points?

Back

Use the points to set up a system of equations and solve for a and b.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.