Tangent line?

Question

G(x) = x^2 - 8x + 10
if
X1=2 & Y1=?

Answer 1

G(x) = x^2 - 8x + 10
=> we can get the slope of tangent line: m = -b/2a
a= coefficients of x^2 which is 1
b= coefficients of x which is -8
so, m = -(-8) / (2*1) = 8/2 = 4

=> we also can get y1 from G(x) equation since we know
x1=2
y1=G(2) = (2)^2 - 8(2) + 10 = 4-16+10= -2

=> now we can get the tangent line equation
we know that tangent line equation: y-y1= m(x-x1)
so, now plug the numbers:
y - (-2) = 4(x-2)
y+2 = 4x - 8
y = 4x - 8 - 2
y = 4x - 6 <======= final answer for tangent line

Answer 2

G'(x) = 2x - 8 which is the slope of the tangent.
At x1 = 2, y1 = x^2 - 8x + 10 = -2
The slope at x1 = 2 = 2(2) - 8 = -4

y = mx + b
-2 = (-4)2 + b
b = 6

equation of tangent line at (2,-2): y = -4x + 6

Answer 3

y = x^2 - 8x + 10
y = x^2 - 8x + 4^2 + 10 - 4^2
y = (x - 4)^2 -6
y + 6 = (x - 4)^2 . . . . . . . this is a parabola facing up
vertex at (4,-6)

when x = 2 , y = 4 - 16 + 10 = - 2
y = -2
tangent line
y ' = 2x - 8
slope = 2(2) - 8 = - 4
slope of tangent line when x = 2 is m = - 4

Answer 4

Y1= G(X1) = 2^2 -8*2 + 10 = -2

Answer 5

g(x) = (2)^2 - 8(2) + 10
y1 = 2 - 16 + 10
= -4

( g(x), f (x) etc always mean y )

I think this is what you mean, i hope.