Suppose a classmate missed the lessons on completing the square to find the center and radius of a circle. Explain the process to that classmate. If it helps, use a problem you’ve already done, as an example.
to access Practice Problem Solutions.
Problem 2
Match each expression with the value needed in the box in order for the expression to be a perfect square trinomial.
\(x^2-8x+\boxed{\phantom{3}}\)
\(x^2+20x+\boxed{\phantom{3}}\)
\(x^2-16x+\boxed{\phantom{3}}\)
\(x^2+9x+\boxed{\phantom{3}}\)
16
20.25
64
100
to access Practice Problem Solutions.
Problem 3
Find the center and radius of the circle represented by the equation \(x^2+y^2+4x-10y+20=0\).
An equation of a circle is given by \((x+3)^2+(y-9)^2=5^2\). Apply the distributive property to the squared binomials and rearrange the equation so that one side is 0.
The triangle whose vertices are \((3,\text-1), (2,4),\) and \((5,1)\) is transformed by the rule \((x,y) \rightarrow (2x,5y)\). Is the image similar or congruent to the original figure?
The image is congruent to the original triangle.
The image is similar but not congruent to the original triangle.
The image is neither similar nor congruent to the original triangle.
