jakhunter354
18.03.2021 •
Mathematics
COPY - Select ALL the systems of equations that have MANY SOLUTION
O a.
Sy =
= 3x + 1
Wy=-3x + 7
b.
Sy = 3x + 1
U= x+1
ſy = 3x + 1
b= 3x + 7
O d.
fx + y do 10
(2x + 2y = 20
Of.
fx+y = 10
(x + y = 12
Solved
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Ответ:
You will have to read to get the 4 main points and the axis of symmetry.
Step-by-step explanation:
Let's get the roots out of the way first. The first thing to try is just factoring it.
The x^2 factors have opposite signs so you get
(x )(-x )
The next problem is to deal with the 3. It has only numbers making it up: itself and 1. So we can pud the 3 somewhere, but where. But we know that the signs on the three must be the same +1 and + 3 or - 1 and - 3. It is a pure guess. on which will work
(x 3)(-x + 1) The minus and plus are just place holders. And finally the 2.
(x + 3)(-2x + 1). Now the only way you can check this is to foil it.
-2x^2 - 6x + x + 3
-2x^2 - 5x + 3
We have the factors. This was just guess work.
Roots
x+3 = 0
x = - 3 is one root.
-2x + 1 = 0
- 2x = -1
x = 1/2
Answer for roots (1/2,0)(-3,0)
============================
Now we go for the vertex.
1. take out - 2 only for the first 2 terms.
y = -2(x^2 + (5/2)x ... ) + 3 The three goes outside the brackets.
2. Take the coefficient inf front of the x. 1/2 it and square the results. Add that inside the brackets
y = -2(x^2 + (5/2)x + (5/4)^2 ) + 3
3. Whatever you do inside the brackets, you have to made an adjustment for after the 3. You also have to take the - 2 into account. These last 2 later.
(5/4)^2 square 5/4(25/16) This goes inside the bracketsy = -2[x^2 + (5/2)x + (25/16)] + 34. What goes after the 3?
-2(25/16) = - 25/8 This is what essentially goes after the three. But should it be minus?The answer is no. That was something the - 2 brought in with it. Since the - 2 makes 25/8 minus, we should be putting +25/8 after the three. That will mean we have added nothing to the equation.y = - 2 (x^2 + (5/2)x + 25/16) )+ 3 + 25/8 Combiney = - 2 (x^2 + (5/2)x + 25/16) ) + 6.1255. Write the vertex form of the equation.
y = -2(x + 5/4)^2 + 6.126
The vertex = (-5/4, 6.125
====================
The axis of symmetry is
x + 5/4 = 0
x = - 5/4
Y intercept
x = 0
y = -2(0)^2 - 5(0) + 3
y intercept = (0,3)
Graph
Red line with the 4 major points is y = -2x^2 - 5x + 3
Blue line is the axis of symmetry x = -5/4
and the coordina" />