The equation of a parabola is given. y=−14x2+4x−19 What are the coordinates of the vertex of the parabola?
1 answer:
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
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