The value of M in the equation (y+5)=(x−2)^2 is 8 if the graph passes through the point (1, 3).
In the given equation (y+5)=(x−2)^2, the expression (x−2)^2 represents a parabola that is shifted horizontally by 2 units to the right. The constant term 5 vertically shifts the parabola upward by 5 units.
To find the value of M, we compare this equation to the standard form of a parabola:
y=a(x−h)^2+k
where (h,k) is the vertex of the parabola. In this case, (h,k)=(2,−5).
The given equation is in the form (y+5)=(x−2)^2, which means the vertex form would be y=(x−2)^2−5. The value of M is the coefficient of (x−h)^2, which is 1.
So, the equation with M would be y=M(x−2)^2−5. If the graph passes through the point (1, 3), we can substitute these values into the equation:
3=M(1−2)^2 −5
Solving for M:
3=M(−1)^2 −5
3=M−5
M=8
Therefore, the value of M is 8 in the equation (y+5)=(x−2)^2 if the graph passes through the point (1, 3).
Complete ques:
What is the value of M in the equation (y+5)=(x−2)^2 if the graph passes through the point (1,3)?