1 answer:
You might be interested in
Answer:
Step-by-step explanation:
Let x be the number of weeks that it will take Andy to reach his goal.
We have been given that Andy currently runs a total of 12 miles per week. He plans to increase that number by 1.5 miles, so number of miles increased in x weeks will be 1.5x and total number of miles ran in x weeks will be 1.5x+12.
Since Andy wants to reach a total of 26 miles per week, so we will equate the total number of miles ran in x weeks with 26.
Therefore, the equation can be used to determine x, the number of weeks that it will take Andy to reach his goal.
We know that
the equation of a parabola is of the form
y=a*(x-h)²+k--------> is a vertical parabola
(h,k) is the vertex
y=−14x²<span>+4x−19
</span><span>Factor the leading coefficient </span>
y=-14*(x²-4/14x)-19
y=-14*(x²-2/7x)-19
<span>Complete the square Remember to balance the equation </span>
y=-14*(x²-2/7x+(1/49)-(1/49))-19
y=-14*(x²-2/7x+(1/49))-19+14/49
the vertex of the parabola is
h=(1/7)-----> 0.1429
k=(-917/49)----> -18.7143
the vertex of the parabola is
(0.1429, -18.7143)
see the attached figure
the equation of a parabola is of the form
y=a*(x-h)²+k--------> is a vertical parabola
(h,k) is the vertex
y=−14x²<span>+4x−19
</span><span>Factor the leading coefficient </span>
y=-14*(x²-4/14x)-19
y=-14*(x²-2/7x)-19
<span>Complete the square Remember to balance the equation </span>
y=-14*(x²-2/7x+(1/49)-(1/49))-19
y=-14*(x²-2/7x+(1/49))-19+14/49
<span>Rewrite as perfect squares</span>
y=-14*(x-1/7)²-917/49the vertex of the parabola is
h=(1/7)-----> 0.1429
k=(-917/49)----> -18.7143
the vertex of the parabola is
(0.1429, -18.7143)
see the attached figure