how to write a equation of a parabola with a vertex at (5,0) and passes through point (1,0)

Question

If I was given a graph with a parabola and the vertex was at (5,0) and it passes through point (1,0) what would be the equation

Answer 1

Since we are given the vertex, we can use the vertex form to find the equation.

 

In vertex form the equation of a parabola is

 

y = a(x - h)² + k

 

where:

a is coefficient of x² term

 

and vertex is in the form (h, k)

 

 

Using our given vertex,

 

h = 5

k = 0

 

Plug this into the vertex form of equation.

 

y = a(x - 5)²

 

 

Next, we need to find the value of a.  We can use the other point the parabola passes through (1, 0).  This point is the x-intercept.  Plug in these values into the vertex form.

 

0 = a(1 - 5)²

 

0 = a(-4)²

 

0 = 16a

 

0 = a

 

 

Then plug in this value of a into the vertex form.

 

y = 0(x - 5)²

 

 

According to these values, there is no equation for this graph.  Here is why.  The vertex lies on the x-axis at x=5.  This means that the graph will not cross any other points that lie on the x-axis.