Quadratic Functions - Definition & Examples
Read this topicExplanations 3
- (Video) An Introduction to Quadratic Functions by Randy Anderson Randy Anderson has a good video introduction to quadratic functions. Summary\large{\text{Summary}}Summary Quadra…
By Ben Ferrara, Alex Federspiel, Joshua Siktar, Amy Feraco, Jonathan Heller, Anusha Rahman, Caroline K
- A quadratic function is simply a function which has degree 222. Check out the explanations for Standard Form and Degree if you need a refresher on this terminology. Now, when wr…
By Vatsal Ojha, Victor Wang, Jonathan Heller, Caroline K, Anusha Rahman
- Quadratic Functions Quadratic functions have the standard form: f(x)=ax2+bx+cf(x)=ax^2+bx+cf(x)=ax2+bx+c where a,b,a, b,a,b, and ccc are constants and a≠0.a\neq 0.a=0. Quadrati…
By Caroline K
Problems 29
- Which of these are quadratic expressions written in standard form?
- Let y1(x)=x2−4x+3y_1(x)=x^2-4x+3y1(x)=x2−4x+3 and y2(x)=x2−4+3xy_2(x)=x^2-4+3xy2(x)=x2−4+3x. Are the two functions y1,y2y_1,y_2y1,y2 the same?
- Which expression is equivalent to −13(32x2−6)-\frac{1}{3}(\frac{3}{2}x^2-6)−31(23x2−6)?
- If you put y=2x2+12−3(x−4)y=2x^2+12-3(x-4)y=2x2+12−3(x−4) into standard form, y=ax2+bx+cy=ax^2+bx+cy=ax2+bx+c, what are aaa, bbb, and ccc respectively?
- Using the Zero Product Property, find the root(s) of the function y(x)=(x−0.5)(3−6x).y(x) = (x-0.5)(3-6x).y(x)=(x−0.5)(3−6x). Select all that apply.
- Check all below that are quadratic functions of ttt.
- Is this a quadratic function? 3x2+6x+1=73x^2+6x+1=73x2+6x+1=7
- Is this a quadratic function? 5x2+2x+1=05x^2+2x+1=05x2+2x+1=0
- Is this a quadratic function? f(x)=x2+3x+2f(x)=x^2+3x+2f(x)=x2+3x+2
- Is this a quadratic function? −x2=9-x^2=9−x2=9
- Is this a quadratic function? f(x)=x+3−2f(x)=x+3-2f(x)=x+3−2
- Is this a quadratic function? (x−3)2=6(x-3)^2=6(x−3)2=6
- Is this a quadratic function? (x−3)=(x+3)(x-3)=(x+3)(x−3)=(x+3)
- Is this a quadratic function? x−2x+9=2\frac{x-2}{x+9} = 2x+9x−2=2
- What is the highest power to which a variable in a quadratic function is taken?
- If the function f(x)=ax2+bx+cf(x)=ax^2+bx+cf(x)=ax2+bx+c is quadratic, what do we know about the value of aaa?
- If the function f(x)=ax3+bx2+cx+df(x)=ax^3+bx^2+cx+df(x)=ax3+bx2+cx+d is quadratic, what do we know about the value of aaa?
- If the function f(x)=ax2+bx+cf(x)=ax^2+bx+cf(x)=ax2+bx+c is quadratic, which of its coefficients could possibly be equal to zero? (Select all that apply.)
- Let f(x)=3x2+4x+1f(x)=3x^2+4x+1f(x)=3x2+4x+1 and g(x)=−x2+2x−1g(x)=-x^2+2x-1g(x)=−x2+2x−1. How would you write the function h(x)=f(x)+g(x)h(x)=f(x)+g(x)h(x)=f(x)+g(x) in standar…
- Let f(x)=6x2+3x+2f(x)=6x^2+3x+2f(x)=6x2+3x+2 and g(x)=3x2+2x−1g(x)=3x^2+2x-1g(x)=3x2+2x−1. How would you write the function h(x)=f(x)−g(x)h(x)=f(x)-g(x)h(x)=f(x)−g(x) in standar…
- Let f(x)=3x2+5x+8f(x)=3x^2+5x+8f(x)=3x2+5x+8 and g(x)=−3x2+x−1g(x)=-3x^2+x-1g(x)=−3x2+x−1. Is the function h(x)=f(x)+g(x)h(x)=f(x)+g(x)h(x)=f(x)+g(x) quadratic?
- Use the zero product property to find the roots of: f(x)=(6x−18)(−9x+45)f(x)=(6x-18)(-9x+45)f(x)=(6x−18)(−9x+45)
- Can you write a function (in its most expanded form) showing the area of the new design?
- Can you write a function showing the area of the new design?
- Lydia is helping Cameron record his sales. She decides to factor the function for simpler calculations. \\ Write the function in factored form.
- Determine which of the following functions is equivalent to the function y=x2−7.y=x^2-7.y=x2−7.
- Evaluate the function f(x)=(x−5)2+5f(x) = (x-5)^2 + 5f(x)=(x−5)2+5 at x=5x=5x=5.
- Which of the following is a quadratic equation?
- Let the area-perimeter differential of a square be the square's area minus its perimeter. What is the minimum value of the area-perimeter differential (as a function of the side…