Graph the equation.y=2(x−4)2+5y=2(x−4) 2 +5
1 answer:
Answer:
Step-by-step explanation:
I believe you meant y = 2(x − 4)^2 + 5. Use the symbol ' ^ " to indicate exponentiation. This equation has the vertex form of the equation of a quadratic. The x-coordinate of the vertex is 4 and the y-coordinate is 5. Thus, the vertex is at (4, 5). The multiplier 2 stretches the graph vertically by a factor of 2.
To aid us in graphing this function, find the x- and y-intercepts:
If x = 0, y = 2(-4)^2 + 5, or 37. Therefore the y-intercept is at (0, 37).
If y = 0, then
2(x − 4)^2 + 5 = 0,
2(x − 4)^2 = -5 But a square cannot be negative, so there is no x-intercept in this case.
To graph this function, plot the vertex (4, 5) and the y-intercept (0, 37). Take advantage of symmetry and find another point across x = 4 from (0, 37): It is (8, 37).
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Answer
• x = –1
• y = –2
• z = 1
Explanation
Given the system:
We have to divide equation 1 over 5 and add it to equation 2:
Now, we have to add 1/5(equation 1) to equation 2:
Next, we multiply the equation 2 obtained previously times 5:
Then, we divide equation 2 over 4:
We add it to equation 3:
Then, we are left with:
Simplifying:
Now that we have the value of z (z = 1), we can replace it in the modified equation 2 and solve for y:
Finally, calculating the value of x with any of the equations (as we already have the other two values):