Question

How do you write \[y = - 10{x^2} + 2\] in vertex form?

Answer 1

Hint: We use the formula of vertex form of a quadratic equation and substitute the value of vertex in the required place and the point through which the quadratic equation passes at required place. Compare the given quadratic equation with general vertex form and write the value of vertex.
* Vertex form of a quadratic equation having vertex \[(h,k)\] and passing through the point \[(x,y)\] is given by \[y = a{(x - h)^2} + k\]

Complete step-by-step answer:
We are given the quadratic equation in the question as \[y = - 10{x^2} + 2\]
We know adding or subtracting ‘0’ will bring no change in the equation, so we can add or subtract 0 from the equation.
We can also write the equation given in the question as \[y = - 10{(x - 0)^2} + 2\] so as to make it appear like a vertex form of the quadratic equation.
Comparing this equation to the general quadratic equation in vertex form i.e. \[y = a{(x - h)^2} + k\] we can write \[a = - 10;h = 0;k = 2\]
Substitute the value of h, k and a in the equation \[y = a{(x - h)^2} + k\] and write the general quadratic equation in vertex form.
\[ \Rightarrow y = - 10{(x - 0)^2} + 2\]

\[\therefore \] We can write \[y = - 10{x^2} + 2\] in vertex form as \[y = - 10{(x - 0)^2} + 2\]

Note:
Many students make mistake of converting the right hand side of the equation given in the question by completing the square formula as they add and subtract same value to make the bracket along with x similar to an identity of \[{(a + b)^2}\] or \[{(a - b)^2}\]. Keep in mind we do not need to perform such steps as we are not given any value with ‘x’. If we were given a complete quadratic equation of the form \[a{x^2} + bx + c\] then we would have completed the square to form \[{(a + b)^2}\]or \[{(a - b)^2}\].