Parabolas! axis of symmetry at x=-7 a maximum height of 4 and also passes through the point (-6,0) write the equation of the parabola in vertex form, will award a medal and fan !

Question

jjuden · Answer

The vertex form of the equation is y = a(x - h)2 + k

anonymous · Answer

okay so what would be a, h , and k?

anonymous · Answer

You have to solve for a by plugging in things you know. (h,k) is the vertex, (x,y) can be any point you have. axis of symmetry is also the x coordinate of the vertex, maximum height is the y value of the vertex so you have a vertex of (-7,4)

so plugging in things we know...
vertex (-7,4)
point (-6,0)

0=a(-6-(-7))+4

can you solve for a?

anonymous · Answer

Forgot my squared...

0=a(-6-(-7))^2+4

jjuden · Answer

Since the axis of symmetry is a vertical line, x = -7 and the parabola has a maximum height of 4 units above the x axis; we can safely conclude that it opens down and its vertex is at (-7, 4). Besides, it passes through the point (-6, 0), which is below the vertex; definitively, it opens down.  Furthermore, if it would open up, it would have a minimum height, not a maximum; so, no arguments, it opens down. 

The vertex form of the equation is y = a(x - h)2 + k  

Since the vertex is defined as (h, k), h = -7 and k = 4:

y = a(x - (-7))2 + 4   or:  y = a(x + 7)2 + 4 

We just need to find the value of "a" (which must be negative, remember, it opens down).  Here is where we use the point through which the parabola passes through: (-6, 0).

We substitute the values x = -6, y = 0 in the equation and solve for a:

0 = a(-6 + 7)2 + 4      simplify and subtract 4 on both sides of the equation:

-4 = a(1)2     or  a = -4  Now we are ready to write our completed equation:

y = -4(x + 7)2 + 4

anonymous · Answer

okay wow thank you both can I like give one of you a medal and the other gives the other one?

jjuden · Answer

sure