Question

How do you graph $y = 5{x^2}$?

Answer 1

Hint: A parabola is defined as a curve in which every point is at a fixed distance from a fixed point and a fixed straight line. The fixed point is called the focus and the fixed straight line is called the directrix. The equation of a parabola is of the form $y = k{x^2}$ , from this equation we observe that a parabola passes through the origin, is U-shaped and y is always positive. The given equation is the equation of a parabola. So, using the above knowledge we will plot the graph of the given parabola.

Complete step-by-step answer:
We have to graph $y = 5{x^2}$
We will put different values of x and obtain the corresponding values of y.We can find the two points by putting random values of one variable and finding out the value of the other variable from the given equation. To find the graph of a straight line, coordinates of two points lying on the straight line are enough but to find the graph of a curve, we need more coordinates to observe the pattern.
At $x = 0,\,y = 5{(0)^2} = 0$
At $x = 1,\,y = 5{(1)^2} = 5$
At $x = 2,\,y = 5{(2)^2} = 20$
At $x = - 1,\,y = 5{( - 1)^2} = 5$
At $x = - 2,\,y = 5{( - 2)^2} = 20$
Using these points, we can plot the graph of $y = 5{x^2}$ as –

Note: A graph shows the relation between two variable quantities, it contains two axes perpendicular to each other namely the x-axis and the y-axis. Each variable is measured along one of the axes. In the question, we are given one linear equation containing two variables namely x and y, x is measured along the x-axis and y is measured along the y-axis while tracing the given equations.