The vertex is when x=-b/2a, which is also the line of symmetry.
in this case, b=6, a=3, so x=-6/6=-1
when x=-1. y=3-6-1=-4
another way to do it is to write the equation into vertex form by making a square:
3x²+6x-1
3(x²+2x-1/3)
3(x²+2x+1-1-1/3))
3(x²+2x+1-4/3))
notice the bold part makes a square:
3(x+1)²-4
Either way,
the vertex is (-1, -4)
the axis of symmetry is x=-1
the coefficient of x² is 3, a positive number, so this parabola opens upward. the function has a minimum value of y=-4
the range is all real number larger than -4
Answer:
2a-3 and a+4
Step-by-step explanation:
Given the equation
2a²+8a -15 = 3a - 3
We are to find one of its factors
Equate the expression to zero
2a²+8a -15 = 3a - 3
2a²+8a -15 - 3a + 3 = 0
Collect the like terms
2a²+8a - 3a - 15 + 3= 0
2a²+5a - 12= 0
Factorize
2a²+8a-3a - 12= 0
2a(a+4)-3(a+4) = 0
(2a-3)(a+4) = 0
Hence the factors are 2a-3 and a+4
Answer:
Exact form: -173/36
Decimal form: -4.805
Mixed number form: -4 29/36
Step-by-step explanation:
Answer:
see explanation
Step-by-step explanation:
(5)
Since ∠EBA = 90° then ∠ABD = 90° ( straight angle ) and
∠ABC + ∠CBD = ∠ABD, that is
2x + 3x - 10 = 90, simplifying
5x - 10 = 90 ( add 10 to both sides )
5x = 100 ( divide both sides by 5 )
x = 20, thus
∠ABC = 2x = 2 × 20 = 40°
∠CBD = 3x - 10 = (3 × 20) - 10 = 60 - 10 = 50°
(6)
4x - 18 = 3x + 7 ( vertical angles are congruent )
Subtract 3x from both sides
x - 18 = 7 ( add 18 to both sides )
x = 25
7y = 5y + 28 ( vertical angles are congruent )
Subtract 5y from both sides
2y = 28 ( divide both sides by 2 )
y = 14
