Question

The original Volkswagen Beetle follows
a quadratic curve, write an equation if
the height is 5 feet long and the length
is 14 feet long. Show your work in the
sketchpads below.

Answer 1

Answer:

$y= -\frac{5}{49}x^{2}+5$

Step-by-step explanation:

In order to solve this, we need to start by drawing a sketch of what the problem looks like (see attached picture).

From the picture, we can see that the graph of the equation should be a parabola with a vertex located at the point (0,5) and x-intercepts located at (-7,0) and (7,0) respectively.

So, there are two ways in which we can build a quadratic equation:

Standard form:

$y=ax^{2}+bx+c$

or

Vertex form:

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

Since we already have the vertex and two points on the equation, we can directly use the vertex form. Where vertex is located at the coordinates (h,k)

So in this case: h=0 and k=5, which simplifies our equation a lot:

$y=a(x-0)^{2}+5$

$y= ax^{2}+5$

So we only need to find the value of a for our equation to be complete. We can use either x-intercept to find this. Let's use the point (7,0) so we get:

$0=a(7)^2+5$

and now we can solve for a:

$-5=49a$

$a=-\frac{5}{49}$

so this completes our equation:

$y= -\frac{5}{49}x^{2}+5$

whose graph looks like the one in the attached picture.