Answer:
vertex ( [tex]\frac{1}{7}[/tex], [tex]\frac{131}{7}[/tex]).
Step-by-step explanation:
Given : The equation of a parabola is given.
y=−14x²+4x−19
To find : What are the coordinates of the vertex of the parabola.
Solution : We have given that
y = −14x²+4x−19
we will be "completing the square" .
Factor out -14 to make leading coefficient 1
y = -14 ([tex]x^{2} -\frac{2x}{7} +\frac{19}{14}[/tex])
Add and subtract [tex](\frac{-1}{7}) ^{2}[/tex]
y = -14 ([tex]x^{2} -\frac{2x}{7} +\frac{19}{14}+\frac{-1}{7}) ^{2} - (\frac{-1}{7})^{2})[/tex] .
Complete the square
y = -14 ( [tex](x -\frac{1}{7}) ^{2} +\frac{19}{14}- (\frac{-1}{7})^{2})[/tex].
y = -14 ( [tex](x-\frac{1}{7}) ^{2} -\frac{131}{7}[/tex]
Standard form of parabola vertex form y = a(x - h)²+ k,
Where, ( h, k) are vertex
On comparing a = -14 , h= [tex]\frac{1}{7}[/tex], k = [tex]\frac{131}{7}[/tex]
Therefore, vertex ( [tex]\frac{1}{7}[/tex], [tex]\frac{131}{7}[/tex]).
