Question

Find the Quadratice function alt="y=a(x-h)x^{2}" align="absmiddle" class="latex-formula"> with given vertex (5,8) and given point (1,3)

Answer 1

Given:

Consider the quadratic function is

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

With given vertex (5,8) and given point (1,3).

To find:

The equation of quadratic function.

Solution:

The quadratic function is

$y=a(x-h)^2+k$               ...(i)

Where, (h,k) is the vertex and a is a constant.

Vertex is (5,8). So,

$(5,8)=(h,k)$

$h=5,k=8$

Putting $h=5,k=8$ in (i), we get

$y=a(x-5)^2+8$           ...(ii)

The given point is (1,3). Putting x=1 and y=3 in  (ii), we get

$3=a(1-5)^2+8$

$3-8=a(-4)^2$

$-5=16a$

$-\dfrac{5}{16}=a$

Putting $a=-\dfrac{5}{16}$ in (ii), we get

$y=-\dfrac{5}{16}(x-5)^2+8$

Therefore, the required quadratic function is $y=-\dfrac{5}{16}(x-5)^2+8$.