Question 272940: Please help me solve this equation: 
I need to find the x intercept and the y intercept and the vertex.
Answer by persian52(161)   (Show Source):
You can put this solution on YOUR website! In detail how to Find the X and Y Intercept.
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y=-3x^(2)-6x-5
To find the x-intercept, substitute in 0 for y and solve for x.
(0)=-3x^(2)-6x-5
Since x is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
-3x^(2)-6x-5=(0)
Any expression with zero in the numerator is zero.
-3x^(2)-6x-5=0
Multiply each term in the equation by -1.
-3x^(2)*-1-6x*-1-5*-1=0*-1
Simplify the left-hand side of the equation by multiplying out all the terms.
3x^(2)+6x+5=0*-1
Multiply 0 by -1 to get 0.
3x^(2)+6x+5=0
Use the quadratic formula to find the solutions. In this case, the values are a=3, b=6, and c=5.
x=(-b\~(b^(2)-4ac))/(2a) where ax^(2)+bx+c=0
Substitute in the values of a=3, b=6, and c=5.
x=(-6\~((6)^(2)-4(3)(5)))/(2(3))
Simplify the section inside the radical.
x=(-6\2i~(6))/(2(3))
Simplify the denominator of the quadratic formula.
x=(-6\2i~(6))/(6)
First, solve the + portion of \.
x=(-6+2i~(6))/(6)
Simplify the expression to solve for the + portion of the \.
x=(-3+i~(6))/(3)
Next, solve the - portion of \.
x=(-6-2i~(6))/(6)
Simplify the expression to solve for the - portion of the \.
x=(-3-i~(6))/(3)
The final answer is the combination of both solutions.
x=(-3+i~(6))/(3),(-3-i~(6))/(3)
To find the y-intercept, substitute in 0 for x and solve for y.
y=-3(0)^(2)-6(0)-5
Expand the exponent (2) to the expression.
y=(-3*0^(2))-6(0)-5
Squaring a number is the same as multiplying the number by itself (0*0). In this case, 0 squared is 0.
y=(-3*0)-6(0)-5
Multiply -3 by 0 to get 0.
y=(0)-6(0)-5
Multiply -6 by each term inside the parentheses.
y=(0)+0-5
Solve the equation.
y=-5
These are the x and y intercepts of the equation y=-3x^(2)-6x-5.
Answer: No x-intercept, y=-5
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Solved for x
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y=-3x^(2)-6x-5
Since x is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
-3x^(2)-6x-5=y
To set the left-hand side of the equation equal to 0, move all the expressions to the left-hand side.
-3x^(2)-6x-y-5=0
Multiply each term in the equation by -1.
-3x^(2)*-1-6x*-1-y*-1-5*-1=0*-1
Simplify the left-hand side of the equation by multiplying out all the terms.
3x^(2)+6x+y+5=0*-1
Multiply 0 by -1 to get 0.
3x^(2)+6x+y+5=0
Use the quadratic formula to find the solutions. In this case, the values are a=3, b=6, and c=1y.
x=(-b\~(b^(2)-4ac))/(2a) where ax^(2)+bx+c=0
Substitute in the values of a=3, b=6, and c=1y.
x=(-6\~((6)^(2)-4(3)(1y)))/(2(3))
Simplify the section inside the radical.
x=(-6\2~(-3(y-3)))/(2(3))
Simplify the denominator of the quadratic formula.
x=(-6\2~(-3(y-3)))/(6)
First, solve the + portion of \.
x=(-6+2~(-3(y-3)))/(6)
Simplify the expression to solve for the + portion of the \.
x=(-3+~(-3(y-3)))/(3)
Next, solve the - portion of \.
x=(-6-2~(-3(y-3)))/(6)
Simplify the expression to solve for the - portion of the \.
x=(-3-~(-3(y-3)))/(3)
The final answer is the combination of both solutions.
Answer: x=(-3+~(-3(y-3)))/(3),(-3-~(-3(y-3)))/(3)
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