Converting Between Different Forms of a Quadratic
Read this topicExplanations 4
- Quadratics Functions Quadratics are polynomials of degree two. They are in the form ax2+bx+cax^2+bx+cax2+bx+c where a,b,ca,b,ca,b,c are the coefficients of the quadratic. Graphs…
By Fiyi Adebekun, Victor Wang
- A quadratic equation will be seen in several different forms. These forms are the standard form of a quadratic, vertex form, and slope-intercept form. They are useful for perfor…
By Vivian Loh, Victor Wang, Anusha Rahman, Jonathan Heller
- (Video) Changing Between Quadratic Forms by Spiffy Math This video by Spiffy Math discusses the pros and cons of each quadratic form, as well as how to convert between the forms…
By Anusha Rahman
- Converting Between Quadratic Forms We can convert between quadratic forms, depending on what we'd need the quadratic for. Given the quadratic equation in factored form: y=2(x+3)…
By Anusha Rahman
Problems 11
- Double Quadratic The quadratic x2−ax+bx^2 - ax + bx2−ax+b has roots p,qp, qp,q and the quadratic x2−px+qx^2 - px + qx2−px+q has roots a,ba, ba,b. Find all possible values of a,b…
- Choose the fewest pieces of information below that can be used to determine the discriminant of a quadratic ax2+bx+cax^2+bx+cax2+bx+c.
- A quadratic P(x)=ax2+bx+cP(x) = ax^2+bx+cP(x)=ax2+bx+c has roots at x=5x = 5x=5 and x=11x = 11x=11. What is the xxx-coordinate of the vertex of PPP?
- Find the vertex of the quadratic polynomial (x+4)(x−2)(x+4)(x-2)(x+4)(x−2).
- A quadratic equation x2+bx+cx^2 + bx + cx2+bx+c has roots b≠0b\neq 0b=0 and c≠0c\neq 0c=0. Compute 10b+c10b+c10b+c.
- A quadratic function y=ax2+bx+cy = ax^2+bx+cy=ax2+bx+c passes through the points (1,h)(1,h)(1,h) and (−1,k)(-1,k)(−1,k). If h−k=12h-k = 12h−k=12, what is bbb?
- Consider the quadratic function f(x)=ax2+bx+cf(x) = ax^2 + bx + cf(x)=ax2+bx+c Assume that aaa and bbb are given. If the function has only one distinct root, what must ccc be?
- Let f(x)=−x2+bx+cf(x)=-x^2+bx+cf(x)=−x2+bx+c. The equation f(x)=0f(x)= 0f(x)=0 has solutions uuu and −v-v−v, where u>0u>0u>0 and v>0v > 0v>0. Given u+v=4u+v=4u+v=4, what is the …
- Find the equation of a quadratic function that has zeros at x=−1x=-1x=−1 and x=1x=1x=1.
- Find the vertex of: y=4x2−16x+14y = 4x^2 - 16x + 14y=4x2−16x+14
- For the function y=ax2−bx+cy = ax^2 - bx + cy=ax2−bx+c, is the vertex a minimum or maximum? Assume a≠0a\neq0a=0.