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sveta [45]
2 years ago
5

How to change from standard for to vertex form

Mathematics
2 answers:
zalisa [80]2 years ago
8 0
If the equation is y = 3(x + 4)2<span> - 6, the value of h is -4, and k is -6. To convert a quadratic from y = ax</span>2<span> + bx + c </span>form to vertex form, y = a(x - h)2+ k, you use the process of completing the square. Let's see an example. Convert y = 2x2<span> - 4x + 5 into </span>vertex form<span>, and state the </span>vertex<span>.</span>
Arlecino [84]2 years ago
8 0
Standard form is
ax^2+bx+c=y
to change to vertex form
complete the square

HOW TO COMPLETE THE SQUARE
first, isolate the x terms
(ax^2+bx)+c=y
factor out a
a(x^2+(b/a)x)+c=y
take 1/2 of the coefient of the x term and square it
(b/a) time 1/2=b/(2a), square it, \frac{b^2}{4a^2}
now add positive and negative inside parenthasees
a(x^2+(b/a)x+\frac{b^2}{4a^2}-\frac{b^2}{4a^2})+c=y
factor perfect square
a(((x+ \frac{b^2}{4a^2})^2-a\frac{b^2}{4a^2})+c=y
distribute
a(x+ \frac{b^2}{4a^2})^2 -a \frac{b^2}{4a^2}+c=y
 a(x+ \frac{b^2}{4a^2})^2 - \frac{b^2}{4a}+c=y
that is vertex form and how to complete the square

for ax^2+bx+c=y
vertex form is
 a(x+ \frac{b^2}{4a^2})^2 - \frac{b^2}{4a}+c=y
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