Solving Quadratic
`x^2-4x+4=0`
`(x-2)^2=0`
Out of the four methods to solve, which method is most efficient to use for
`x^2-36=0`
Square Root Method
Solve the system
`y=-x^2+9`
`y=2x+6`
`(-3, 0), (1, 8)`
When is
`x^2-36<=0`
`(oo, -6]U[6, oo)`
:(
:)
`x^2-49=0`
`(x-7)(x+7)=0`
Out of the four methods to solve, which method is most efficient to use for
`x^2-8x+16=0`
Factoring
Find the solution(s) to the following system
`y=x^2-6x+10`
`y=4-x`
`(3, 1), (2, 2)`
When is
`x^2>5x+6`
`(oo, -1)U(6, oo)`
No one is going to choose this so whatever
blah
`3a=-11a-6`
`(x+3)(3x+2)=0`
Out of the four methods to solve, which method is most efficient to use for
`4v^2+7v-7=0`
Quadratic Formula
What is the solution(s) to the following system
`y=x^2-6x+7`
`y=-2x+3`
`(2, -1)`
What is the solution to
`2x^2-x+4>0`
What are the four ways to solve quadratics and choose a method to create and example on when it would be most efficient to solve.
Square Root, Factoring, Complete the Square, Quadratic Formula.
`2x^2-3x+11=0`
`x=(3+-isqrt(77))/4`
`-r^2=5x+50 `
Quadratic Formula
Solve for the solution(s) to the system below.
`y=3x^2-7x+1`
`y=x-7`
No solution
What is the solution to
`5x^2-15x+10<0`
`(1, 2)`
2 Solutions- Quadratic & Linear Function intersect twice.
1 Solution- Quadratic & Linear Function intersect one time.
No Solution- The Quadratic & Linear Function never intersect.
`2a^2+20=12a`
`a=3+-i`
Out of the four methods to solve, which method is most efficient to use for
`3x^2+12x=-50`
`x=-2+-isqrt(114)/3`
Solve for the solution(s) of the following system.
`y=3x^2+21x-5`
`-10x+y=-1`
`(-4, -41), (1/3, 7/3)`
What is the solution to
`-3x^2+7x-5>=0`
No solution
For quadratic inequalities, how do you tell if you have a special case? In addition, how could you tell the difference between a no solution and infinite solution scenario.
If the discriminant is negative (i) there is a special case. The difference between no solution & infinite solution is determined by the inequality (</>) and the direction of opening for the quadratic.