**andhereicome said: Hi! Um, I was hoping to get some help with my math homework... I'm supposed to solve the equation y=-2x^2+16x-30 by graphing by hand, using my calculator, factoring, and by using the quadratic formula, and I'm pretty lost. Thank you!**

Basically its asking you to find for what x values will y = 0 using various methods.

Let’s start with factoring.

First set the equation to zero giving us: **0=-2x^2+16x-30**

Next we can immediately notice we can immediate* factor out the -2* from the right side. This gives us **0=-2(x^2-8x+15)**

Now we have to figure out what two numbers can we multiply together to get 15 and add together to get -8. Well the factors of 15 are (-1,-15) (1,15) (3,5) **(-3,-5)** (-1,-15) and (1,15). Of all of these we will** use -3 and -5** because they* both add to negative 8* and *multiply to make 15*. This means the equations they can be factored as **(x-3)*(x-5)**. So now we have found the **0=-2(x-5)(x-3)**

Now all we have to do is solve for x, but we have two solutions. First divide by -2 on both sides, giving us **0=(x-5)(x-3)**. Now we have to take each expression and solve for x, so now we have:

x-5=0

x-3=0

This gives us

x=5

x=3

You have completed the problem by factoring.

To graph by hand. since we already know the answer you can simply graph by **plugging in integer values**. Since we already know the answer it would be best to plug in x=0 to x=5. After getting your values, plot them, and you can see that **y=0 at x=3 and x=5**.

Your graph should look like this.

To do the quadratic formula method, use the quadratic formula make **-2=a, 16=b, -30=c**

Use this equation:

\

Lots of algebra later you have x=3 and x=5. If you need help solving the equation let me know. *(+/-) by the way means there are two solutions, one solution using the addition and a separate solution using subtraction*.

Using your calculator will vary by your model of calculator but I’d suggest graphing the function and finding where the function crosses y=0. This will be at x=3 and x=5. Similar to graphing by hand but much faster.

Hope this helps if you need anything more in depth, feel free to ask.

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