problems involving quadratic functions

[ashley_sagaert]

i need help how to figure out these

determine the equation of the parabola with x-intercepts
a) -4 and 3, and that passes through (2,7)

questions like that and instead of given x-intercepts you are asked hte same but with the vertex.

how can i solve this?

thanks for your help!
Ashley

 

[jwpaine]

Setup a system of equations to solve for all coefficients a,b,c in ax^2 + bx + c

{a (-4)^2 + b (-4) + c = 0 <----- for your x intercept
{a (3)^2 + b (3) + c = 0 <----- for your x intercept
{a (2)^2 + b (2) + c = 7 <----- for your ordered pair

Solve the system of equations for a, b and c. This will give you an equation for the parabola that passes through the ordered pair, (2,7) and has x = {-4 , 3} as roots.

And for the vertex, x = -b/(2a)

Cheers,
John

 

[Mrspi]

i need help how to figure out these

determine the equation of the parabola with x-intercepts
a) -4 and 3, and that passes through (2,7)

questions like that and instead of given x-intercepts you are asked hte same but with the vertex.

how can i solve this?

thanks for your help!
Ashley

Here's another approach. If a parabola has x-intercepts at "p" and "q", then the equation of the parabola can be written in INTERCEPT FORM as follows:

y = a(x - p)(x - q)

You are given that this parabola intersects the x-axis at -4 and 3. Substitute -4 for p, and 3 for q:

y = a(x - (-4))(x - 3)
y = a(x + 4)(x - 3)

Now, all that is needed to complete the equation is the value of "a". Fortunately, we are told that the point (2, 7) is on the parabola. Substitute 2 for x, and 7 for y:

7 = a(2 + 4)(2 - 3)
7 = a(6)(-1)
7 = -6a
-7/6 = a

So....the equation of the parabola is

y = (-7/6)(x + 4)(x - 3)


You mention that you have another problem in which you are given the VERTEX of the parabola, and a point on the parabola. For this problem, you may want to use the VERTEX form of the parabola with vertex at (h, k):

y = a(x - h)^2 + k

You can substitute the coordinates of the vertex for h and k. Then, you can substitute the coordinates of the given point for x and y, which will enable you to find the value of "a".....