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Basic Algebra - Quadratic Equations

For 1-3 solve the equation using the square root property
1. (m+1)^2 = -1
2. (p-1)^2 = 12
3. (t+5)^2 = -18
For 4 & 5, find the value of n such that the expression is a perfect square trinomial, then factor it.
4. X^2 -9X+n
5. Z^2 -2/5z +n
For 6-8, solve the equation by completing the square and applying the square root property
6. 3X^2 + 2X +1 = 0
7. W^2 + 4W = -13
8. b^2 + 7/2b = 2
For 9-11, write the function in the vertex form of a parabola and give the coordinates of the vertex, X-intercepts, y- intercepts and sketch a graph by hand.
9. P(x) = -5X^2 -10X -13
10. Z(x) = X^2 -6X +7
11. q(x) = -3X^2 -24X -54

Solution Preview

For 1-3 solve the equation using the square root property
(m+1)2 = -1
Solution:
(m+1)^2=-1
Taking square root on both sides:
√((m+1)^2 )=√(-1)
Or,(m+1)=±√(-1)
Or,m=-1±√(-1)

(p-1)2 = 12
Solution:
(p-1)^2=12
Taking square root on both sides:
√((p-1)^2 )=√12
Or,(p-1)=±2√3
Or,p=1±2√3

(t+5)2 = -18
Solution:
(t+5)^2=-18
Taking square root on both sides:
√((t+5)^2 )=√(-18)
Or,(t+5)=±√(-18)
Or,t=-5±√(-18)

For 4 & 5, find the value of n such that the expression is a perfect square trinomial, then factor it.
X2 ...

Solution Summary

The expert solves an equation using the square root property. The value of n such that the expression is a perfect square trinomial is given.

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