Question

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

Answer 1

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 \\ (2)/(4)=(4a)/(4) \\ a=(1)/(2) \end{gathered}`

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

`y=(1)/(2)(x-1)^2+3`

Hence, the equation of the parabola is:

`y=(1)/(2)(x-1)^(2)+3`

or

`y=(x^2-2x+7)/(2)`