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Find the Vertex (h, x) using this formula

h space equals space minus fraction numerator b over denominator 2 a end fraction o f space f left parenthesis x right parenthesis space equals space minus 2 x to the power of 2 space end exponent plus space 4 x space minus space 7 space

(1, 5)

(-1, 5)

(1, -5)

(2, -7)

Respuesta :

Answer:

The correct option is C.

Step-by-step explanation:

If a parabola is defined as

[tex]f(x)=ax^2+bx+c[/tex]          .... (1)

then the vertex of the parabola is

[tex]Vertex=(-\frac{b}{2a},f(-\frac{b}{2a}))[/tex]

The given function is

[tex]f(x)=-2x^2+4x-7[/tex]          .... (2)

From (1) and (2) it is clear that

[tex]a=-2,b=4,c=7[/tex]

[tex]h=-\frac{b}{2a}[/tex]

Substitute a=-2 and b=4 in the above equation.

[tex]h=-\frac{4}{2(-2)}=-\frac{4}{-4}=1[/tex]

The value of h is 1.

substitute h=1 in function (2).

[tex]f(1)=-2(1)^2+4(1)-7=-5[/tex]

The vertex of the function is (1,-5). Therefore the correct option is C.

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