Exam Review #2 AT HOME

Front

Write the equation of a circle with center (h, k) and radius r.

Back

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

Front

What is the center and radius of the circle given by the equation: x^2 + y^2 + 14x - 2y = -1?

Back

To find the center and radius, rewrite the equation in standard form. Completing the square gives: Center = (-7, 1), Radius = 7.

Front

Describe the transformation of the equation y = a|x - h| + k from the parent function y = |x|.

Back

The transformations include: 1. Vertical stretch/shrink by |a|, 2. Reflection over the x-axis if a < 0, 3. Horizontal shift right by h, 4. Vertical shift up by k.

Front

What is the vertex of the parabola given by the equation y = a(x - h)^2 + k?

Back

The vertex of the parabola is the point (h, k).

Front

Convert the equation -3x + 4y = 12 into slope-intercept form (y = mx + b).

Back

The slope-intercept form is: $$y = \frac{3}{4}x + 3$$.

Front

What does it mean for a function to be reflected over the x-axis?

Back

A reflection over the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

What is the standard form of a circle's equation?

Back

The standard form of a circle's equation is $$(x - h)^2 + (y - k)^2 = r^2$$, where (h, k) is the center and r is the radius.

Front

How do you find the center of a circle from its equation in standard form?

Back

The center (h, k) can be found directly from the equation $$(x - h)^2 + (y - k)^2 = r^2$$.

Front

What is the effect of a negative coefficient in front of the absolute value function?

Back

A negative coefficient reflects the graph over the x-axis.

Front

What is the formula for the distance between two points (x1, y1) and (x2, y2)?

Back

The distance formula is: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$.