Simple Quadratic Factor question

  • Context: High School 
  • Thread starter Thread starter james_rich
  • Start date Start date
  • Tags Tags
    Quadratic
Click For Summary
SUMMARY

The discussion focuses on solving the quadratic equation y = -x² + 5x + 6 and finding the coordinates of its vertex. The correct factorization is y = -(x + 1)(x - 6), leading to x-intercepts at x = -1 and x = 6. The vertex is calculated as (5/2, 49/4) using both the vertex formula and completing the square method. The initial arithmetic error was identified, clarifying that the correct y-value at the vertex is 49/4, not 99/4 or 29/4 as previously suggested.

PREREQUISITES
  • Understanding of quadratic equations and their standard form.
  • Familiarity with the vertex formula for parabolas.
  • Basic algebraic skills, including factorization and completing the square.
  • Knowledge of arithmetic operations involving fractions.
NEXT STEPS
  • Study the process of completing the square for quadratic functions.
  • Learn about the vertex form of a quadratic equation.
  • Explore the properties of parabolas, including symmetry and intercepts.
  • Practice solving quadratic equations using various methods, including factoring and the quadratic formula.
USEFUL FOR

Students studying algebra, educators teaching quadratic functions, and anyone seeking to improve their problem-solving skills in mathematics.

james_rich
Messages
23
Reaction score
0
okay i need to solve the quadratic y = -x^2 + 5x + 6 and need to find the coordinates of the vertex of the curve

by factorising

y = -(x^2 - 5x - 5)
y = -(x + 1)(x - 6)

so when y = 0, x = -1 and x = 6 (that parts simple)
..............
At the vertex x = (-1 + 6) / 2 = 5/2 (as the curve is symetrical)

so as y = -x^2 + 5x + 6

y = -5/2^2 + 5(-5/2) + 6
y = 25/4 + 50/4 + 24/4
y = 99/4

(this is the answer i got which doesn't look right, and answer book gives a different answer)

can u tell me where i went wrong? thanx
 
Mathematics news on Phys.org
Sorry, this sites changed a bit since i last came on, I've posted it in the wrong section
 
y = -5/2^2 + 5(-5/2) + 6
y = 25/4 + 50/4 + 24/4
First line should read -(5/2)^2+5(5/2)+6
Second line should read -25/4+50/4+24/4
Result y=49/4
I suggest you carefully check your arithmetic before posting.
 
thanx i got that answer too, wasn't sure which way to work it out, the negative sign threw me a bit, the book is wrong then as i thought, they have 29/4 for their answer!

thanx for ur help
 
mathman is right & here's why:
-5/2*5/2=-25/4 because -1*1=-1
5 * 5/2 = 25/2 = 50/4
6 = 24/4
50 + 24 - 25 = 50 - 1 = 49/4
There's your answer
 
You can also do this by completing the square:
y= -x2+ 5x+ 6= -(x2- 5x)+ 6
= -(x2- 5x+ 25/4- 25/4)+ 6
= -(x- 5/2)2+ 25/4+ 6
= -(x- 5/2)2+ 25/4+ 24/4
= -(x- 5/2)2+ 49/4

The vertex is at (5/2, 49/4).
 

Similar threads

MHB Which Quadratic Function Has Exactly One X-Intercept?
  • · Replies 3 ·
Replies
3
Views
2K
High School Strange quadratic manipulation
  • · Replies 6 ·
Replies
6
Views
2K
High School Natural Numbers contain all the Primes
  • · Replies 24 ·
Replies
24
Views
3K
High School About a definition: What is the number of terms of a polynomial P(x)?
  • · Replies 48 ·
2
Replies
48
Views
4K
MHB 5.t.11 find x for the imaginary factors
  • · Replies 2 ·
Replies
2
Views
1K
MHB The Minimum Value of a Quadratic Function: A Question of Symmetry
  • · Replies 3 ·
Replies
3
Views
2K
High School Solving the Heart Curve Equation: 'y =
  • · Replies 18 ·
Replies
18
Views
4K
High School Quadratic with simple meaningful intuitive constants
  • · Replies 2 ·
Replies
2
Views
2K
High School So many people are unable to do simple algebra
  • · Replies 10 ·
Replies
10
Views
2K
MHB Solving 8 Roots: Can 3 Quadratic Polynomials Fulfill $f(g(h(x)))=0$?
  • · Replies 1 ·
Replies
1
Views
1K