Question

te each problem in Level 3!LT#3) (3T) Write the equation of a parabola that has a vertex of(3,2) and has an x-intercept at (1,0). (LT #3)

Answer 1

We know that

• The vertex is (3,2).

,

• The x-intercept is at (1,0).

The vertex form of a parabola equation is-

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

Where h and k are the coordinates of the vertex.

We use the given information to find the parameter a,

$\begin{gathered} 0=a(1-3)^2+2 \\ -2=a(-2)^2 \\ -2=4a \\ a=-\frac{2}{4}=-\frac{1}{2} \end{gathered}$

So, a is equal to -1/2.

We already have all the parameters to write the equation for the parabola in vertex form because h = 3, k = 2, and a = -1/2.

$y=-\frac{1}{2}(x-3)^2+2$