So since the vertex falls onto the axis of symmetry, we can just solve for that to get the x-coordinate of both equations. The equation for the axis of symmetry is , with b = x coefficient and a = x^2 coefficient. Our equations can be solved as such:
y = 2x^2 − 4x + 12:
y = 4x^2 + 8x + 3:
In short, the vertex x-coordinate's of y = 2x^2 − 4x + 12 is 1 while the vertex's x-coordinate of y = 4x^2 + 8x + 3 is -1.
Answer:
Ryan would like to eat <em>more than</em> 50 carbs per day, but <em>no more than</em> 150 carbs per day.
So, Ryan's total carb intake must be <em>between </em>50 and 150 carbs.
Step-by-step explanation:
So he wants to keep his consumption of carbs between the inequalities:
So, let's solve both inequalities.
1)
Subtract 10 from both sides:
Divide both sides by 2:
2)
Subtract 10 from both sides:
Divide both sides by 2:
So, our inequality is now:
Since we solved the equations:
Written as a compound inequality, this is:
In other words, Ryan would like to eat <em>more than</em> 50 carbs per day, but <em>no more than</em> 150 carbs per day.
So, Ryan's total carb intake must be <em>between </em>50 and 150 carbs.