Graphing and Transforming Parabolas using the Directrix and Focus
Read this topicExplanations 3
- (Video) Transformations of Parabolas by Mrclarkmath Here's a video by Mrclarkmath explaining the translations of a parabola and what they mean. Summary aaa can tell you the gene…
By Alex Federspiel, Anusha Rahman
- ###Transforming a Parabola‾\underline{\textbf{Transforming a Parabola}}Transforming a Parabola There are Three Types of Transformations: Given,y=(x)2\text{Given,}\quad y = (x)^…
By Mia, Anusha Rahman
- Transforming Parabolas We know that a parabola is a curved shape that can be described by a special rule involving a focus and directrix. The focus is a fixed point inside the c…
By Anusha Rahman
Problems 14
- Suppose bbb is a real number and f(x)=3x2+bx+12f(x) = 3x^2 + bx + 12f(x)=3x2+bx+12 is a function such that f(1)=f(3)f(1) = f(3)f(1)=f(3). What is f(5)f(5)f(5)?
- What is the minimum value of f(x)=x2−6xf(x) = x^2-6xf(x)=x2−6x for real values of xxx?
- If the vertex of the parabola y=x2−12x+cy= x^2 - 12x + cy=x2−12x+c is on the xxx-axis, what is ccc?
- Suppose we have a parabola represented by the equation x=ay2x = ay^2x=ay2. If we reflect this across the line y=−xy=-xy=−x, then what is the equation of this new parabola?
- True or False\text{True or False}True or False === The parabola y=(x−3)2+6y=(x-3)^2+6y=(x−3)2+6 is graphed above.
- True or False\text{True or False}True or False === The parabola x=y2−3y+1x=y^2-3y+1x=y2−3y+1 is graphed above.
- What is the equation of the parabola above?
- What is the equation of the parabola above?
- What is the equation of the new (red) parabola?
- A parabola with the equation y=x2y=x^2y=x2 is shifted down 4 and to the right 6. What is the new equation of the parabola?
- A parabola with the equation y=x2y=x^2y=x2 is shifted down 4 and to the right 6 and then reflected over the line y=xy=xy=x. What is the new equation of the parabola?
- True or False\text{True or False}True or False === If f(x)=2(x−3)2+1f(x)=2(x-3)^2+1f(x)=2(x−3)2+1 and c=−5c=-5c=−5 then f(cx)f(cx)f(cx) is graphed above.
- True or False\text{True or False}True or False === If f(x)=−(x−2)2+4f(x)=-(x-2)^2+4f(x)=−(x−2)2+4 and c=3c=3c=3 then f(x+c)f(x+c)f(x+c) is graphed above.
- A parabola has the equation f(x)=2(x−3)2+1f(x)=2(x-3)^2+1f(x)=2(x−3)2+1. What does f(x)+cf(x)+cf(x)+c do to the graph?