Question

The equation of a parabola is given.

Answer 1

Answer:

vertex (  $\frac{1}{7}$, $\frac{131}{7}$).

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 ($x^{2} -\frac{2x}{7} +\frac{19}{14}$)

Add and subtract $(\frac{-1}{7}) ^{2}$

y = -14 ($x^{2} -\frac{2x}{7} +\frac{19}{14}+\frac{-1}{7}) ^{2} - (\frac{-1}{7})^{2})$ .

Complete the square

y = -14 ( $(x -\frac{1}{7}) ^{2} +\frac{19}{14}- (\frac{-1}{7})^{2})$.

y = -14 ( $(x-\frac{1}{7}) ^{2} -\frac{131}{7}$

Standard form of parabola vertex form y  = a(x - h)²+ k,

Where, ( h, k)  are vertex

On comparing a = -14 , h= $\frac{1}{7}$, k =  $\frac{131}{7}$

Therefore, vertex (  $\frac{1}{7}$, $\frac{131}{7}$).

Answer 2

The coordinates are 8, -3.