Answer:
m = -22
Step-by-step explanation:
Formula for parabola in it's vertex form is given by;
y = a(x - h)² + k
Where (h, k) is the coordinate of the vertex.
We are told that vertex is at (-6, 6) and the roots are at 10 and m.
Thus;
y = a(x - (-6))² + 6
y = a(x + 6)² + 6
Since 10 is a root, thus;
0 = a(10 + 6)² + 6
-6 = 256a
a = -6/256
a = -3/128
Thus,the equation is;
y = (-3/128)(x + 6)² + 6
Since m is a root, then;
0 = (-3/128)(m + 6)² + 6
-6 = (-3/128)(m + 6)²
Rearranging, we have;
128 × 6/3 = (m + 6)²
256 = m² + 12m + 36
m² + 12m - 256 + 36 = 0
m² + 12m - 220 = 0
Using quadratic formula, we have;
m = 10 or -22
The issue here is to express fractions more easily:
2 <span>1/4: 6 3/4
lets simplify fractions:
</span>2 <span>1/4 = 8/4 + 1/4 = 9/4
6 3/4 = 24/6 + 3/4 = 27/6
So the ratio can also be expressed as:
</span><span>9/4 : </span>27/6
lets find a common denominator:
54/24 : 108/24
are also equivalent, so we can reduce:
54 : 108
and finally
1 : 2
Answer:
Step-by-step explanation:
