Answer:
The missing measurement is :
= ~ 12
=> Original height should be : 7+12 =19
Answer:
axis of symmetry is
.
The ordered pair of the vertex is
.
Step-by-step explanation:
Your function is a quadratic.
Compare
to
.
You should see that
.
The x-coordinate of the vertex or the axis of symmetry since the axis symmetry goes through the vertex can be found by computing
.
So here we go!
The axis of symmetry is
.
When you write your axis of symmetry be sure to write it as an equation.
That is the axis of symmetry is
.
Now that was also the x-coordinate of your vertex. To find the corresponding y-coordinate of the vertex, plug your value for
into
.

Put into calculator:
when 
The ordered pair of the vertex is
.
Answer:
A) - Quartic polynomial
- has four roots
- roots are; f(x) = (x + 5i)(x - 5i)(x + 2)(x - 2)
B) - Cubic polynomial
- has 3 roots
- roots are; f(x) = (x - 5)²(x + 5)
Step-by-step explanation:
A) f(x) = x⁴ + 21x² − 100
The highest power in this polynomial is 4 and thus, it is called a quartic polynomial. This means that it will have 4 roots.
Factorizing this polynomial gives;
f(x) = (x² + 25)(x² - 4)
Equating to zero, we can find the roots. Thus, the roots are;
x = 5i
x = -5i
x = 2
x = -2
Thus, the completely factorized polynomial is;
f(x) = (x + 5i)(x - 5i)(x + 2)(x - 2)
B) f(x) = x³ − 5x² − 25x + 125
The highest power in this polynomial is 3. It is therefore a cubic polynomial with 3 roots.
Factorizing this polynomial gives;
f(x) = (x² - 25)(x - 5)
Equating to zero and Factorizing gives;
x = 5
x = -5
x = 5
Thus, completely factorized with the roots is;
f(x) = (x - 5)²(x + 5)