many questions help! (1 Viewer)

[Mr Chi]

Can someone show me how to work any of these out?

1) y= x^2-10x+5 (complete the square)

2) x^2-5x+ 6=0 (find roots of quadratic equation)

3) y=x^2-4x-10 (sketch parabola)

4) gradient function of curve is f'(x) = 6x^2-6x-12

... find the values of x for which the curve rises with downward concavity.

5) Use simpsons rule with 5 function values..from x=1 to x=3 on the curve y=4^-x

If someone can help me with any of these it would be great, thanks

 

[jemsta]

1) x^2-10x+5
= x^2-10x+25+5
= (x-5)^2 +5

2) x^2-5x+6=0
(x-3)(x-2)
therefore x=3, or x=2

3)x^2-4x-10 use quadratic formula and ull get ur roots as 2+sqrt14 and 2-sqrt14
for y just sub in x=0 and youll get -10
therefore since u know where the roots for the x and y axis are then just draw the parabola

4) f'(x)= 6x^2-6x-12
therefore when curve rises with downward concavity, f''(x)<0
therefore f''(x)= 12x-6
12x-6<0
12x<6
x<1/2

 

[pLuvia]

5) Use simpsons rule with 5 function values..from x=1 to x=3 on the curve y=4^-x

∫ 4^-x dx ≈ 1/3[4^-1+4[4^-1.5+4^-2.5]+2[4^-2]+4^-3
= 65/152

 

[webby234]

1) x^2-10x+5
= x^2-10x+25+5

Shouldn't it be
x^2 - 10x + 25 + 5 - 25 (you have added 25, therefore you have to subtract 25)
So y = (x-5)^2 - 20
or y + 20 = (x-5)^2