How to do you graph #y = 2x^2 + x - 3# by plotting points?

Question

Nathan Axel · Accepted Answer

Vertex, #(-0.25,-3.125)#, axis of symmetry, #x= -0.25#
x intercepts, #(-1.5,0) and (1,0)#, y intercept, # (0 ,-3)#,
additional point, # (-2,3)# #y= 2 x^2+x-3 or y= 2(x^2+0.5 x)-3 # or #y= 2{x^2+0.5 x+(0.25)^2}-0.125-3 # or #y= 2(x+0.25)^2-3.125 # ,this is vertex form of equation , #y=a(x-h)^2+k ; (h,k)# being vertex , here #h=-0.25 ,k=-3.125,a=2 #, therefore vertex is at # (-0.25, -3.125)#, since #a# is positive, parabola opens upward. Axis of symmetry is #x= h or x = -0.25 ; # , y-intercept is found by putting #x=0# in the equation #y=2 x^2_x-3 or y=-3# y intercept is at # (0 ,-3)# x-intercepts are found by putting #y=0# in the equation # 2 x^2+x-3=0 or 2 x^2 -2 x +3 x -3= 0# or #2 x( x-1) +3(x-1)=0 or (x-1) (2 x+3) =0 # #:. x= 1 , x= -3/2 =-1.5# , x-intercepts are at #(-1.5,0) and (1,0)#. Additional point: #x=-2, y = 2 (-2)^2+ (-2)-3= 3 or (-2,3)# graph{[-10, 10, -5, 5]} [Ans] = 2x^2+x-3

Hazel Anglin · Answer

#" "#
Please read the explanation.

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We have the quadratic equation #color(red)(y=f(x)=2x^2+x-3#

Create a data table of values as shown below:

In the following table,

you can see Column 1 (with x values) and

Column 4 (with the corresponding y values) are shown:

Plot all the values from the table, to create the graph:

Obviously, from the table, for the value of #color(red)(y=0)#,

there are two corresponding #color(red)(x# values.

Hence, #color(blue)((-1.5,0) and (1.0,0))# are the x-intercepts..

Values in the shaded area are shown on the graph:

We will examine the Vertex and the Axis of Symmetry in the following graph:

#color(red)("Vertex :" (-0.25,-3.125)#

#color(blue)((0, -3)# is the y-intercept..

Axis of Symmetry is at :#color(blue)((x=-2.5)#

Hope you find the solution process useful.

Julia Adams · Answer

undefined To graph the equation y = 2x^2 + x - 3 by plotting points, you can choose various x-values, plug them into the equation to find the corresponding y-values, and then plot these points on a coordinate plane. You can start by selecting a range of x-values, such as -3, -2, -1, 0, 1, 2, and 3, and then calculate the corresponding y-values using the equation y = 2x^2 + x - 3. After obtaining the pairs of x and y values, plot them on a coordinate plane and connect the points to form a curve.