Answer:
Step-by-step explanation:
Vertex-form equation for vertical parabola:
y = a(x-h)² + k
with
vertex (h,k)
axis of symmetry: x = h
Apply your equation
y = 3x² + 18
vertex (0,18)
axis of symmetry: x = 0
Answer:
x = - 6 or x = 2
Step-by-step explanation:
The absolute value function always returns a positive value. However, the expression inside can be positive or negative.
Given
| 2x + 4 | - 1 = 7 ( add 1 to both sides )
| 2x + 4 | = 8, thus
2x + 4 = 8 ( subtract 4 from both sides )
2x = 4 ( divide both sides by 2 )
x = 2
OR
-(2x + 4) = 8
- 2x - 4 = 8 ( add 4 to both sides )
- 2x = 12 ( divide both sides by - 2 )
x = - 6
As a check
Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.
x = 2 → | 4 + 4 | - 1 = | 8 | - 1 = 8 - 1 = 7 ← True
x = - 6 → | - 12 + 4 | - 1 = | - 8 | - 1 = 8 - 1 = 7 ← True
Hence the solutions are x = - 6 or x = 2
the 1st one is the right answer.
The roots routine will return a column vector containing the roots of a polynomial. The general syntax is
z = roots(p)
where p is a vector containing the coefficients of the polynomial ordered in descending powers.
Given a vector
which describes a polynomial
we construct the companion matrix (which has a characteristic polynomial matching the polynomial described by p), and then find the eigenvalues of it (which are the roots of its characteristic polynomial)
Example
Here is an example of finding the roots to the polynomial
--> roots([1 -6 -72 -27])
ans =
12.1229
-5.7345
-0.3884
