Quadratic Functions Question - Find in Form of y = ax2 + bx + c

Hey All

Got a test tomorrow, I'd appreciate some help. I'm pretty good in math but I just don't get these questions here.

Find, in the form y = ax2 + bx + c, the equation of the quadratic whose graph:

q1) touches the x-axis at 4 and passes through (2,12)

q2) has vertex (-4, 1) and passes through (1, 11)

You need to have 2 equations for the 2 different situations. It's the same technique but I just don't know it. Any help appreciated!!

Re: Quadratic Functions Question - Find in Form of y = ax2 + bx + c

Quote:

Originally Posted by

**JemDkyl** Hey All

Got a test tomorrow, I'd appreciate some help. I'm pretty good in math but I just don't get these questions here.

Find, in the form y = ax2 + bx + c, the equation of the quadratic whose graph:

q1) touches the x-axis at 4 and passes through (2,12)

q2) has vertex (-4, 1) and passes through (1, 11)

You need to have 2 equations for the 2 different situations. It's the same technique but I just don't know it. Any help appreciated!!

Vertex point is given by

If graph passes through point then

So you have to solve system of three equations with three unknowns in each case .

Re: Quadratic Functions Question - Find in Form of y = ax2 + bx + c

That wasn't very helpful :/ Could you solve one for me and I'll do the other one myself? I need to see an example, that's how I get things :P

Re: Quadratic Functions Question - Find in Form of y = ax2 + bx + c

Re: Quadratic Functions Question - Find in Form of y = ax2 + bx + c

-b/2a = 4

b = -8a

Then I replace 2 with x and y with 12?

4a + 2b + c = 12

16a + 4b + c = 0 (x intercept replaced)

-----------------

12a + 2b = -12

Since b is -8a --> 12a + 2(-8a) = -12

-4a = - 12

a = 3

Afterwards I just replace 3 with a in the previous 12 + 2b = -12 equation.

b = -24

I find c the same way, it's 48.

So I guess the final equation should be y = 3x2 - 24x + 48

I still don't understand the theory though.. why is -b/2a = 4??

Isn't 4 the x-intercept, but not the minimum/maximum point of the graph?

Re: Quadratic Functions Question - Find in Form of y = ax2 + bx + c

It's both.

As for the vertex, we have

Completing the square would give:

.

You should know that the vertex of a quadratic of the form (known as the vertex form of a quadratic) is and this is what we have here. and

If you're still unsure as to why this is the case, you should probably consult an instructor.

Re: Quadratic Functions Question - Find in Form of y = ax2 + bx + c

Alright I get it then. I'll solve a few more problems like this one, the thread can be closed now. Thanks! :)