QUESTION THAT I HAD TROUBLE WITH...
Solve this by using the Quadratic Formula: 0= 3x² + 4x + 5
My answer
Quadratic Formula:
Then I subbed in the variables with:
a= 3 b=4 c=5
When I was square rooting the number I got after doing b² - 4ac, I noticed that I wasn't getting an answer. I got really frustrated, I thought I made a mistake in my calculations.
Help
When my teacher took this question up on the board he taught me that this question actually had no answer, so my calculations were right.
My teacher showed me a technique to check before starting the quadratic formula called discriminant.
D= b² - 4(a)(c)
When I would plug my values into this and get my answer, just by looking at the answer I would know how many solution I would get if there were any for the problem.
1) If the number is less than 0, there will be no solutions
2) If the number is more than 0, there will be 2 solutions
3) If the number is 0, there will be only 1 solution
PRACTICE
1) For the following: State what type of factoring and solve.
a. 12x² + 9x + 15 b. 36m² - 121 c. 17x² + 34x + 51
d. x² - 16x + 64 e. 25 - m² f. 4 - 12y + 9y²
g. x² + 4 h. n² - 14n +49 i. 13m + 26m²+ 39
j. x² + 5x + 6 k. 2x² - 3x - 35 l. 2n² + 3n - 9
2) For the following: Solve using the Quadratic Formula
a. 2x² - 3x - 5= 0 b. m² - 5m - 14= 0 c. 4b² + 8b + 7= 4
d. 2m² - 7m - 13= -10 e. x² + 4x + 3= 0 f. 2x² - 3x - 15= 5
3) For the following: Solve using the Quadratic Formula but make sure to check if there is a solution using the dicriminant.
a. 3x² + 4x + 7= 0 b. h² - 11h + 30= 0 c. z² + 6z + 14= 0
d. 5x² + 9x + 7= 0 e. 5m² - 12m + 18 = 5 f. 4x² + 11x -20 =0
Here is a video..
WORLD PROBLEMS
1) The equation for a soccer ball kicked in the air by Oscar is h= 4t² + 22t + 50. Where t is the time in seconds and h is the height.
a. Practice writing this formula in factored and vertex form
b. When does the ball hit the ground?
c. What was the highest point the ball reached?
2) Write an equation for the parabola with a vertex at (-2,0), a vertical stretch of 4 and opening downwards
3) A football is kicked up at 10.2 meters/second, from a height of 2m above ground. The height of the football above the ground, after "t" seconds is shown by the equation -5.2t² + 10.2t + 2
a. What is the amount of time it took the football to hit the ground?
b. What is the time when the football is 5m above the ground?
c. What is the maximum height of the football and at what time does it reach that height?