What is the vertex form of y= 3x^2+29x-44 ?
1 Answer
Explanation:
Method 1 - Completing the Square
To write a function in vertex form (
-
Make sure you factor out any constant in front of the
x^2 term, i.e. factor out thea iny=ax^2+bx+c .
y=3(x^2+29/3x)-44 -
Find the
h^2 term (iny=a(x-h)^2+k ) that will complete the perfect square of the expressionx^2+29/3x by dividing29/3 by2 and squaring this.
y=3[(x^2+29/3x+(29/6)^2)-(29/6)^2]-44
Remember, you cannot add something without adding it to both sides, that is why you can see(29/6)^2 subtracted. -
Factorise the perfect square:
y=3[(x+29/6)^2-(29/6)^2]-44 -
Expand brackets:
y=3(x+29/6)^2-3×841/36-44 -
Simplify:
y=3(x+29/6)^2-841/12-44
y=3(x+29/6)^2-1369/12
Method 2 - Using General Formula
From your question,
Therefore,
Substituting