Understanding Parabolas As Translations Page 2
ADVERTISEMENT
1
2
3
43. A quadratic function can be put into vertex form by a process called
completing the square. Watch the steps below that put the given
quadratic function in vertex form.
Notice what a perfect square looks like multiplied out
b
b
b
b
x +
= x +
x +
= x + bx +
2
2
2
2
b
b
b
b
x
= x
x
= x
bx +
2
2
2
2
(Start with a quadratic equation like below)
y = 2x
12x + 23
(Subtract the constant from both sides)
y
23 = 2x
12x
(Factor out the leading coefficient from the right-hand side)
y
23 = 2(x
6x)
(Complete the square inside the parenthesis - this means
adding the same number on the left. Watch out - this is the
hardest part!)
y
23 + 2(9) = 2(x
6x + 9)
(Write the right-hand side as a perfect square)
y
5 = 2(x
3)
(Move the new constant term back to the right side)
y = 2(x
3) + 5
Now use the vertex formula from lecture to check that the
vertex of y = 2x
12x + 23 is (3,5)
4. Follow the steps above to put a general quadratic equation in vertex
form.
(Start with the quadratic equation below)
y = ax + bx + c
(Subtract the constant from both sides)
(Factor out the leading coefficient from the right-hand side)
2
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education