Question

How do you graph \[y={{x}^{2}}+2x-4\]?

Answer 1

Hint: From the given question we have been asked to find the graph of a function. So, for questions of this type involving finding the graph of a function we will use a substitution method. In this method we will substitute values for x and solve for the value for y. Thus, we will draw the graph of function through the points we found out. So, we proceed with our solution as follows.

Complete step by step solution:
Firstly, for the given function that is \[y={{x}^{2}}+2x-4\] we will substitute the value of x as \[x=-3\]. Then we will find the value of corresponding y.
\[\Rightarrow y={{x}^{2}}+2x-4\]
\[\Rightarrow y={{\left( -3 \right)}^{2}}+2\left( -3 \right)-4\]
\[\Rightarrow y=-1\]
We got the point as \[\Rightarrow \left( -3,-1 \right)\]
Now, similarly we will substitute the value of x as zero and find the corresponding value of y. so, doing that we get,
\[\Rightarrow y={{x}^{2}}+2x-4\]
\[\Rightarrow y={{(0)}^{2}}+2\left( 0 \right)-4\]
\[\Rightarrow y=-4\]
Now, similarly we will substitute the value of x as one that is \[ x=1\] and find the corresponding value of y. so, doing that we get,
\[\Rightarrow y={{x}^{2}}+2x-4\]
\[\Rightarrow y={{\left( 1 \right)}^{2}}+2\left( 1 \right)-4\]
\[\Rightarrow y=-1\]
Here using these points we will draw the graph of given question. It will be a parabola.
The general form of parabola is \[ y=a{{x}^{2}}+bx+c\]. When we compare our given function to this general form our a will be \[a=1\]. Here \[a=1\] is positive. So, we can say that when it is positive the graph of the parabola will open upwards.
So, the graph will be as follows.

Note: Students must be very careful while doing the calculations. Students must have good knowledge in the concept of substitution method and parabola and its applications. Students should not make mistakes like if they don’t know that for a parabola when a is positive it opens upwards then it might be difficult to draw the graph.