Circles and Parabolas 2023 with verified questions and answers

What is the equation for a circle? (x - h)^2 + (y - k)^2 = r^2 What is the midpoint formula? x1+x2/2 ; y1+y2/2 How do you know you are going to Graph a circle? If addition and if the coefficients are the same. How do you get the equation of a circle if it is not in standard form? Group the x and y's together then complete the square. How do you complete the square? Divide the middle coefficient by 2 and square it. Then add it to both sides of the equation. What is the formula for parabolas? (x-h)^2=4p(y-k) How can you tell if the Parabola opens up or down? Opens up if p0 Opens down if p0 What is the formula for a sideways Parabola? (y-k)^2=4p(x-h) What are the steps to Graph a Parabola? Write the standard equation Find the vertex to determine the orientation Find P by solving 4p=coefficient Find focus Plot vertex focus and AOS. Sketch directions using vertical y=k-p or Horizontal x=h-p Use focus, x-value or am x-value near it in a table and solve for the y. Use AOS to plot symmetric point and connect. What is the formula to find p? 4p= coefficient How do you know if a Graph opens up down or sideways? If y is squared it opens sideways. If x is squared it opens up and down. How do you find the focus (side to side) (h+p,k) What is the formula to find the focus (up or down) (h,k+p) What is the formula to find the directrix (vertical) y=k-p What is the formula to find the directrix (horizontal) x=h-p