Answer
The vertex is at point (-3, -1)
The axis of symmetry is x = -3
Explanation
We are asked to find the vertex and axis of symmetry of the equation given.
f(x) = x² + 6x + 8
The vertex of a quadratic equation is the point where the graph of the quadratic equation changes from sloping negatively to sloping positively and vice-versa.
The axis of symmetry represents the straight line that divides the graph of the quadratic equation into two mirror parts that are similar to and are mirror images of each other. This axis of symmetry usually passes through the vertex.
To find the vertex, it is usually at the turning point where the first derivative of the quadratic equation is equal to 0.
(df/dx) = 0
f(x) = x² + 6x + 8
(df/dx) = 2x + 6
At the vertex
(df/dx) = 2x + 6 = 0
2x = -6
Divide both sides by 2
(2x/2) = (-6/2)
x = -3
We then insert this into the equation to get the corresponding f(x) value.
f(x) = x² + 6x + 8
f(-3) = (-3)² + 6(-3) + 8
= 9 - 18 + 8
= -1
Hence, the vertex is at point (-3, -1)
And since the axis of symmetry has to pass through the vertex,
The axis of symmetry is x = -3
Hope this Helps!!!
Answer:
6.75×10^5
Step-by-step explanation:
that's the answerrr
Answer:
1.625 gallons
Step-by-step explanation:
.25(25%) times 6.5
May this help you!!!!!!!!!!!
Answer:
B. increase by a factor of 3.
Step-by-step explanation:
According to ohms law:
V ∝ R
Vo = IoR
R = Vo/Io ... (1)
Vo is the initial potential difference/voltage
Io is the initial current across the resistor
R is the resistance
If for an Ohmic conductor, we triple the voltage without changing the resistance:
New voltage V1 = 3Vo
New voltage V1 = I1R (resistance doesn't change)
I1 is the current after the voltage has tripled
3Vo = I1R
R = 3Vo/I1... (2)
Equating both resistances in 1 and 2 since resistance doesn't change we have:
Vo/Io = 3Vo/I1
1/Io = 3/I1
I1/Io = 3
New current I1 = 3Io
This shows that tripling the voltage increases the current by factor of 3
