Quadratic Graph Example: y=ax²
Read this topicExplanations 3
- The standard form of a quadratic function is the following: y=ax2+bx+cy = ax^2+bx+cy=ax2+bx+c xxx represents an unknown variable, aaa, bbb, and ccc are constants, and a≠0a\ne 0a…
By Catherine Yeo, Grace Carey, Alex Federspiel, Jonathan Heller, Caroline K, Anusha Rahman
- All quadratic functions have the form y=ax2+bx+c,y = ax^2 + bx + c,y=ax2+bx+c, where a,b,ca, b, ca,b,c are real numbers. If any of them are zero, one of the terms goes away. If …
By Joshua Siktar, Victor Wang, Jonathan Heller, Anusha Rahman
- (Video) Algebra 2 4-1 Quadratic Functions and Transformations: Problem 1 - Graphing f(x)=ax2f(x) = ax²f(x)=ax2 by Matthew Richardson This video by Matthew Richardson discusses t…
By Amy Feraco, Jonathan Heller, Caroline K, Anusha Rahman
Problems 26
- We graphed the following functions: y=3x2y=3x^2y=3x2, y=2x2y=2x^2y=2x2, and y=5x2y=5x^2y=5x2. Which of these is the graph of y=2x2y = 2x^2y=2x2?
- Graphed are y=3x2y=3x^2y=3x2, y=5x2y=5x^2y=5x2, and y=4.5x2y=4.5x^2y=4.5x2. Which of these is the graph of y=4.5x2y = 4.5x^2y=4.5x2?
- There are 4 functions plotted above, with graphs y=x2y=x^2y=x2, y=−x2y=-x^2y=−x2, y=3x2y=3x^2y=3x2, and y=−3x2y=-3x^2y=−3x2. Which one is in red?
- There are 444 functions plotted above, with graphs y=x2y=x^2y=x2, y=−x2y=-x^2y=−x2, y=3x2y=3x^2y=3x2, and y=−3x2y=-3x^2y=−3x2. Which one is in black?
- CONCEPT CHECK: Which graph crosses the line x=2x=2x=2 sooner (i.e. for a smaller value of yyy): y=4x2y=4x^2y=4x2 or y=14x2y=\frac{1}{4}x^2y=41x2?
- Above are pictured two graphs of the form y=ax2y = ax^2y=ax2. True or False: The red graph has a smaller ∣a∣|a|∣a∣ value than the blue graph.
- The three graphs above (each of the form y=ax2y = ax^2y=ax2) have different aaa values. Order the graphs from largest to smallest aaa values.
- Consider the quadratic equation y=ax2y=ax^2y=ax2. If a>0a>0a>0, what is the minimum yyy-value of the graph?
- Consider the quadratic equation y=ax2y=ax^2y=ax2. If a<0a<0a<0, what is the maximum y-value of the graph?
- If f(x)=ax2f(x)=ax^2f(x)=ax2 is a quadratic function, what must be true of aaa?
- Which two parabolas are symmetric to one another about the x-axis?
- Which two parabolas are symmetric to one another about the x-axis?
- For what value of aaa does the function f(x)=ax2f(x)=ax^2f(x)=ax2 pass through the point (1,2)(1,2)(1,2)?
- For what value of aaa does the function f(x)=ax2f(x)=ax^2f(x)=ax2 pass through the point (1,−2)(1,-2)(1,−2)?
- For what value of aaa does the function f(x)=ax2f(x)=ax^2f(x)=ax2 pass through the point (2,2)(2,2)(2,2)?
- For what value of aaa does the function f(x)=ax2f(x)=ax^2f(x)=ax2 pass through the point (2,−2)(2,-2)(2,−2)?
- Consider the above graph of f(x)=x2f(x)=x^2f(x)=x2 and g(x)=−x2g(x)=-x^2g(x)=−x2. Which of the following is true? (Check all that apply.)
- Consider the above graph of f(x)=2x2f(x)=2x^2f(x)=2x2 (in red) and g(x)=12x2g(x)=\frac{1}{2}x^2g(x)=21x2 (in blue). Which of the following is true? (Check all that apply.)
- Consider the above graph of f(x)=−2x2f(x)=-2x^2f(x)=−2x2 (in red) and g(x)=−12x2g(x)=\frac{-1}{2}x^2g(x)=2−1x2 (in blue). Which of the following is true? (Check all that apply.)
- Which coordinates below give the vertex of any quadratic function of the form y=ax2y=ax^2y=ax2?
- If y=−x2y = -x^2y=−x2 was graphed, in which direction would the parabola open?
- If y=4x2y = 4x^2y=4x2 was graphed, in which direction would the parabola open?
- Which of the following parabolas open upward?
- Which of the following parabolas open downward?
- Which of the above graphs has the shape y=ax2y=ax^2y=ax2 where aaa is a positive number?
- Which of the above graphs has the shape y=ax2y=ax^2y=ax2 where aaa is some negative number?