What is the minimum point of the graph of the equation y=2x^2+8x+9 ?
plz help !!!

Question

What is the minimum point of the graph of the equation y=2x^2+8x+9 ?
plz help !!!

satellite73 · Answer

what they are asking for is the second coordinate of the vertex

satellite73 · Answer

the first coordinate of the vertex of $$y=ax^2+bx+c$$ is always $$-\frac{b}{2a}$$

satellite73 · Answer

the second coordinate (what is you are looking for) is what you get when you replace $x$ by $-\frac{b}{2a}$

bellezabrilla · Answer

@statellite73 i wasn't taught how to do it using that method

satellite73 · Answer

in your example $a=2,b=8$ so first find $-\frac{b}{2a}$

satellite73 · Answer

ok i am sure you can also do it by "completing the square" but this method actually will complete the square for you quickly and easily
so if $a=2,b=8$ then what is $-\frac{b}{2a}$?

bellezabrilla · Answer

-2

satellite73 · Answer

yes it is

satellite73 · Answer

so now what is $$y=2(-2)^2+8\times (-2)+9$$?

bellezabrilla · Answer

Y=1

bellezabrilla · Answer

I used the calculator

satellite73 · Answer

yes it is 1 with or without a calculator

satellite73 · Answer

$$y=2(-2)^2+8\times (-2)+9\
2\times 4-16+9\
8-16+9\
-8+9\1$$

satellite73 · Answer

and that is your final answer

bellezabrilla · Answer

(-2,1)

satellite73 · Answer

btw this also means $$y=2x^2+8x+9=2(x+2)^2+1$$

bellezabrilla · Answer

Kk :)

satellite73 · Answer

yes, that is  your "minimum point" or as we "vertex"

satellite73 · Answer

don't forget the magic formula $\color{red}{-\frac{b}{2a}}$

bellezabrilla · Answer

Alrighty THANK YOU so much !!! I really appreciated your help

satellite73 · Answer

yw

bellezabrilla · Answer

Wait... Quick question !

satellite73 · Answer

ok ..

bellezabrilla · Answer

Lol.. okay the "magic formula" can only be used when trying to find the minimum point?

satellite73 · Answer

it is the first coordinate of the vertex of any quadratic , i.e. anything that looks like $$y=ax^2+bx+c$$

satellite73 · Answer

if the parabola opens up, i.e if $a>0$ then it gives the minimum point on the graph 
if the parabola opens down, ie. if $a<0$ it gives the maximum point 
it is real easy to use

satellite73 · Answer

for example if $$y=-3x^2+12x-4$$then $a=-3,b=12$ and $-\frac{b}{2a}=-\frac{12}{2\times (-3)}=2$

satellite73 · Answer

since $$y=-3x^2+12x-4$$ opens down, it would be the first coordinate of the highest point on the graph

bellezabrilla · Answer

Ahh okay I see THANKK YOU SO MUCHH !!! You're simply amazing  😝😝😝

bellezabrilla · Answer

@satellite73

satellite73 · Answer

you are quite welcome
always nice to help with someone who actually participates !!

bellezabrilla · Answer

Wait another question.. this is my last one !!!!

bellezabrilla · Answer

@satellite73 do you have any tips on factoring ?

satellite73 · Answer

yes 
set it equal to zero and solve, then factor

satellite73 · Answer

you mean factoring a quadratic right?  like $$x^2-x-6$$ or sommat

bellezabrilla · Answer

Quadratic

satellite73 · Answer

right 
so in my simple example $$x^2-x+6$$ you need to find two numbers whose product is $-6$ and that add to $-1$ 
since $-6$ is negative one has to be negative, the other positive 
in this case $-3$ and $2$ work because $-3\times 2=-6$ and $-3+2=-1$ so $$x^2-x-6=(x-3)(x+2)$$ but that was a simple one

satellite73 · Answer

if it is harder, use the quadratic formula to find the zeros,then you know how to factor
for example, if you find the zeros are $-\frac{1}{2}$ and $5$ then it factors as $$(2x+1)(x-5)$$

bellezabrilla · Answer

Alrighty :) once again thanks a lot !!

satellite73 · Answer

once again, yw