Question

What is the equation of the parabola with vertex (1,3) and passing through (3,5)?

Answer 1

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given details

$\begin{gathered} vertex(1,3) \\ point(3,5) \end{gathered}$

STEP 2: Write the formula for equation of parabola using vertex and point

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

WHERE:

(h,k) is the vertex

STEP 3: Substitute the values into the formula

$y=a(x-1)^2+3$

STEP 4: Find the value of a by using the point

$\begin{gathered} (3,5)=(x,y) \\ x=3,y=5 \\ By\text{ substitution,} \\ 5=a(3-1)^2+3 \\ 5=a(2^2)+3 \\ 5=4a+3 \\ 5-3=4a \\ 2=4a \\ \frac{2}{4}=\frac{4a}{4} \\ a=\frac{1}{2} \end{gathered}$

STEP 5: Get the equation of the parabola by substituting the values

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

Hence, the equation of the parabola is:

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

or

$y=\frac{x^2-2x+7}{2}$