Step-by-step explanation:
Equation 1: [tex]3x^{2} +7x-6[/tex]
Step 1: Write a quadratic equation in standard form choosing your own coefficients and constant.
Conditons that need to be satisfied: B can be 0 in only one question, parabola should open up and have a negative y intercept.
1. The parabola should open upwards: a> 0
2. [tex]3x^2+7x-6[/tex] (a>0), y-int is negative (0s for x's)
3(0)^2 + 7(0) -6
y= -6
Step 2:
1. Factor the original equation: (3x-2)(x+3)
x=2/3, -3
2. Strategy used (factor by grouping)
Equation 2: -[tex]x^{2}[/tex] + 3x - 6
Equation 2 should represent a parabola that opens down and has a negative y-intercept.
Parabola that opens down = a<0
Ax^2 + Bx + C
-[tex]x^{2}[/tex] + 3x - 6
Negative y-intercept: -(0)^2 +3(0) -6 = y= -6
Strategy to solve: Quadratic formula
Why? - This equation doesn't factor cleanly.
Show your work:
a= -1 b= 3 c= -6
Write the quadratic formula down ([tex]x= \frac{-b + \sqrt{b^{2} - 4ac } }{2a}[/tex]) ± not just +
Show step, solve.
x= 1.5 + 1.9365i
Equation 3:
Sorry, I can't do this.
Equation 4 :[tex]x^{2} -1[/tex]
You decide.
Alright, easy parabola.
1. Does parabola open up or down. UP
2. Is there a vertical stretch or compression? NO
3. What is the y-intercept- (0,-1)
[tex]x^{2} -1[/tex]
Strategy: Simple factoring patterns (Difference of squares) -
(x+1)(x-1)
x = + 1
Show work: x^2 is square of x,
Equation 5: [tex]x^{2} -3x+15[/tex]
x^2−3x+15
a=1 b= -3 c=15
([tex]x= \frac{-b + \sqrt{b^{2} - 4ac } }{2a}[/tex]) ± not just +
Good luck! Sorry that I couldn't do equation 3, vertical stretches are not my thing.
