a quadratic function has zeros at 1 and -3 and passes through the point (2,10). Write the equation in vertex form Hint: write the equation in standard form before vertex form. Hint: write all general formulas which you need to use
- print Print
- list Cite
Expert Answers
briefcaseTeacher (K-12)
calendarEducator since 2011
write3,179 answers
starTop subjects are Math, Science, and Business
A quadratic function has zeros at 1 and -3 and passes through the point (2,10).
(1) First we can write the function in intercept form: `y=a(x-p)(x-q)` where `p,q` are the x-intercepts (zeros, roots, etc...)
Thus we have `y=a(x-1)(x+3)` (Note that if k is a zero of a function, then (x-k) is a factor)
We need to solve for the coefficient a; we use the point (2,10):
`10=a(2-1)(2+3)`
`10=5a`
`a=2`
Thus we have `y=2(x-1)(x+3)`
(2) From here we can write in general form: `y=ax^2+bx+c` by...
(The entire section contains 247 words.)
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
Related Questions
- Write the standard form of the quadratic function that has vertex (-2, 5) and whose graph passes...
- 1 Educator Answer
- How convert a cubic equation in standard form ax^3+bx^2+cx+d to vertex form a(x-h)^3+kI need...
- 1 Educator Answer
- 2x squared -5=4x use quadratic formula write the equation in standard form identify a,b,c...
- 1 Educator Answer
- Solve the equation x^2 - 6x + 5 = 0 use the quadratic formula and factorization.
- 2 Educator Answers
- Write the equation of the quadratic function with roots -10 and -8 and a vertex at (-9, -1).
- 1 Educator Answer