Mathematics: The quadratic function g(x) has a vertex at (-5, 0) and y-intercept of (0, -5). What is g(1)?

100% - 3240% - xANSWER: 40% of 32 = 12,8...

The quadratic function g(x) has a vertex at (-5,

Tywan566

31.01.2022

-7.2

Step-by-step explanation:

The vertex form of quadratic equation : f (x) = m(x - a)^2 + b, where (a,b) is the vertex.

Given: The quadratic function g(x) has a vertex at (-5, 0).

Put (a,b)= (-5,0) for function g(x), we get

$g(x)=m(x-(-5))^2+0\\\\\Rightarrow\ g(x)=m(x+5)^2$

Also, its y-intercept is (0, -5).

Put x= 0 and g(x) =-5

$-5=m(0+5)^2\\\\\Rightarrow\ -5=m(25)\\\\\Rightarrow\ m=\dfrac{-5}{25}\\\\\Rightarrow\ m=\dfrac{-1}{5}$

so, $g(x)=-\dfrac{1}{5}(x+5)^2$

For g(1), put x=1

$g(1)=-\dfrac{1}{5}(1+5)^2\\\\=-\dfrac{1}{5}(6)^2=-\dfrac{1}{5}(36)\\\\=-7.2$

Hence, g(1) is -7.2.

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