1.What is the vertex from the equation?
Y=x^2+12x=4
(Please show your work to show me the steps to get to the right answer.)
2. Use the quadratic formula to solve the equation.
x^2-7x-6=0
(Please show your work to show me the steps to get to the right answer. )
3.simplify the expression
(-2/)(8/)
(Please show your work to show me the steps to get to the right answer. )
Y= x^2+12x=4 ????
I think maybe
y = x^2 + 12 x + 4 ????
x^2 + 12 x = y-4
x^2 + 12 x + (12/2)^2 = y - 4 + 36
(x+6)^2 = y+32
how about (-6,-32)
x^2-7x-6=0
a = 1
b = -7
c = -6
x = [ 7 +/- sqrt {49 -(4)(-7)(-6) } ] /2
= [ 7 +/- sqrt {49 -168 } ] /2
= [ 7 +/- sqrt {-119 } ] /2
are you sure that was not +6 = c ?
-1/4 ????
1. To find the vertex of a quadratic equation in the form y = ax^2 + bx + c, you can use the formula x = -b/2a.
In the given equation y = x^2 + 12x + 4, the coefficients are a = 1, b = 12, and c = 4.
To find the x-coordinate of the vertex, substitute the values into the formula:
x = -b/2a = -12/(2*1) = -6
To find the y-coordinate of the vertex, substitute the x-coordinate back into the equation:
y = (-6)^2 + 12(-6) + 4 = 36 - 72 + 4 = -32
So, the vertex of the equation y = x^2 + 12x + 4 is (-6, -32).
2. The quadratic formula is used to solve a quadratic equation in the form ax^2 + bx + c = 0. The formula is x = (-b ± √(b^2 - 4ac))/(2a).
In the given equation x^2 - 7x - 6 = 0, the coefficients are a = 1, b = -7, and c = -6.
Substitute these values into the quadratic formula:
x = (-(-7) ± √((-7)^2 - 4*1*(-6)))/(2*1)
x = (7 ± √(49 + 24))/(2)
x = (7 ± √(73))/(2)
Therefore, the solutions to the equation x^2 - 7x - 6 = 0 are x = (7 + √73)/2 and x = (7 - √73)/2.
3. To simplify the expression (-2/8), you can simplify the numerator and denominator separately, and then divide.
The numerator, -2, does not have any factors other than 1 and -2.
The denominator, 8, can be simplified to its prime factorization, which is 2 × 2 × 2.
Now, divide the simplified numerator and denominator:
-2/(2 × 2 × 2)
Notice that there are two 2's in both the numerator and denominator, so they can cancel each other out:
-1/2
Therefore, the simplified expression (-2/8) is equal to -1/2.