Question

What is the vertex of $y=2{{x}^{2}}-4x+3$ ?

Answer 1

Here in this question we have been asked to find the vertex of the given equation $y=2{{x}^{2}}-4x+3$ by observing the given equation we can say that it is in the form of a quadratic parabola and from the concepts we know that the vertex of the parabola will be given by substituting $x=\dfrac{-b}{2a}$.

Complete step-by-step solution:
Now considering from the question we have been asked to find the vertex of the given equation $y=2{{x}^{2}}-4x+3$ .
From the basic concepts of quadratic expressions we know that any quadratic expression generally represents a parabola.
By observing the given equation we can say that it is in the form of a quadratic parabola.
From the basic concepts of parabola we know that the vertex of the parabola when the equation is given as $y=a{{x}^{2}}+bx+c$ will be given by substituting $x=\dfrac{-b}{2a}$ and finding the value of the $y$ coordinate.
By observing the given equation we will have $a=2,b=-4,c=3$ .
Therefore the $x$ coordinate of the vertex will be given as $\dfrac{-\left( -4 \right)}{2\left( 2 \right)}=1$.
By substituting $x=1$ in the given equation we will have the $y$ coordinate of the vertex will be given as
$\begin{aligned} & y=2{{\left( 1 \right)}^{2}}-4\left( 1 \right)+3 \\\ & \Rightarrow y=2-4+3 \\\ & \Rightarrow y=1 \\\ \end{aligned}$ .
Therefore we can conclude that the vertex of the given expression $y=2{{x}^{2}}-4x+3$ will be given as $\left( 1,1 \right)$.

Note: While answering questions of this type we should be sure with the concepts that we are going to apply in between the steps in the process. The graph of the given equation will look like: