When Are Two Quadratic Functions Identical?
Read this topicExplanations 3
- Two quadratic functions are identical if their equations are the same, or if they coincide at three distinct points. This is true because there is at most one quadratic through …
By Benjamin Qi
- Two quadratic functions are identical if they coincide at 3 distinct points. This is a good, and accurate definition, but without graphing the entire function, how else can we v…
By Ben Ferrara
- There are two ways to tell if quadratic functions are identical: If their equations, y=f(x)y = f(x)y=f(x), are equivalent If their graphs share 3 points in common Both of these …
By Hannah Bonville, Victor Wang
Problems 14
- Concept Question: How many points do you have to prove two quadratic functions share to say they are identical?
- Which quadratic graph(s) is/are identical to the orange graph shown above? Check all that apply.
- If the quadratic functions y1(x)=−3x2−5x+1y_1(x)=-3x^2-5x+1y1(x)=−3x2−5x+1 and y2(x)=−3x(x+b)+10x+1y_2(x)=-3x(x+b)+10x+1y2(x)=−3x(x+b)+10x+1 are identical, find bbb.
- Suppose f(x)=ax2+bx+cf(x) = ax^2 + bx + cf(x)=ax2+bx+c is a quadratic such that f(0)=1f(0) = 1f(0)=1, f(1)=5f(1) = 5f(1)=5, and f(2)=100f(2) = 100f(2)=100. What is f(−1)f(-1)f(−1)?
- How many points are required to unambiguously specify a quadratic function?
- If aaa, bbb, ccc, ddd, and eee are constants such that for every x>0x > 0x>0, the expression 5x4−8x3+2x2+4x+7(x+2)4\frac{5x^4 - 8x^3 + 2x^2 + 4x + 7}{(x + 2)^4}(x+2)45x4−8x3+2x2…
- How many points on two functions (not necessarily quadratic) are required to be the same in order for us to say that the functions are identical?
- When graphing two identical quadratic functions, one finds that the graphs are
- Are these two formulas identical? f(x)=x2+2x+1f(x)=x^2+2x+1f(x)=x2+2x+1 f(x)=−x2−2x−1f(x)=-x^2-2x-1f(x)=−x2−2x−1
- Are these two functions identical? f(x)=3x2−2x+4f(x)=3x^2-2x+4f(x)=3x2−2x+4 f(x)=−3x2+2x−4f(x)=-3x^2+2x-4f(x)=−3x2+2x−4
- Are these two functions equivalent? y=2x2−x−3y=2x^2-x-3y=2x2−x−3 y=−2x2−x−3y=-2x^2-x-3y=−2x2−x−3
- Are these two functions equivalent? f(x)=82x2−3x+2f(x)=\dfrac{8}{2}x^2-3x+2f(x)=28x2−3x+2 f(x)=4x2−93x−2f(x)=4x^2-\frac{9}{3}x-2f(x)=4x2−39x−2
- Are these two functions identical? f(x)=−(x2−3x+2)f(x)=-(x^2-3x+2)f(x)=−(x2−3x+2) f(x)=−x2+3x−2f(x)=-x^2+3x-2f(x)=−x2+3x−2
- Suppose parabola A and parabola B share a vertex. Does that mean the quadratic functions are identical? Why or why not?