Respuesta :
Answer:
Vertex of the parabola is ( 1 , 14 ).
Step-by-step explanation:
Given Equation of parabola is [tex]y=-2^2+4x+12[/tex]
We have to find the vertex of the parabola.
We first convert the given equation of parabola in standard equation of parabola using completing the square method.
Standard equation of parabola,
[tex](x-h)^2=4a(y-k)[/tex]
here, ( h , k ) is coordinates of the vertex of the parabola.
consider,
y = -2x² + 4x + 12
y = -2( x² - 2x - 6 )
y = -2 ( x² - 2x + 1² - 1² - 6 )
y = -2 ( x -1 )² - 7 × ( -2 )
y - 14 = -2 ( x - 1 )²
[tex](x-1)^2=\frac{1}{2}(y-14)[/tex]
By comparing,
vertex = ( 1 , 14 )
Therefore, Vertex of the parabola is ( 1 , 14 ).
