Answer:
<u>y = -x² + 4</u>
Step-by-step explanation:
The equation of the parabola in the vertex form is:
y = a (x-h)² + k
Where: (h,k) the coordinates of the vertex & a is a multiplier
The parabola has a vertex at ( 0,4 )
So, h = 0 , k = 4
∴ y = a (x-0)² + 4
∴ y = a x² + 4
The parabola passes through points ( 2,0 )
∴ 0 = a 2² + 4
∴ 4 a = -4 ⇒ a = -4/4 = -1
∴ y = -x² + 4
So, the equation of a parabola that has a vertex at ( 0,4 ) and passes through points ( 2,0 ) is <u>y = -x² + 4</u>
See the attached figure.
Answer is 3a²b (a + b)
Step-by-step explanation:
- Step 1: Find 3a² (ab²+b²)
⇒ 3a² (ab²+b²) = 3a³b + 3a²b² = 3a²b (a + b)
Area of a triangle = (height * base ) / 2
height = (Area * 2) / base
height = (49.5 * 2) / 9
height = 99 / 9
height = 10 cm²
28 times 1/7 would give you 4
Given:
The graph of a downward parabola.
To find:
The domain and range of the graph.
Solution:
Domain is the set of x-values or input values and range is the set of y-values or output values.
The graph represents a downward parabola and domain of a downward parabola is always the set of real numbers because they are defined for all real values of x.
Domain = R
Domain = (-∞,∞)
The maximum point of a downward parabola is the vertex. The range of the downward parabola is always the set of all real number which are less than or equal to the y-coordinate of the vertex.
From the graph it is clear that the vertex of the parabola is at point (5,-4). So, value of function cannot be greater than -4.
Range = All real numbers less than or equal to -4.
Range = (-∞,-4]
Therefore, the domain of the graph is (-∞,∞) and the range of the graph is (-∞,-4].
