How do you graph #y=2x^2 -5x -3#?

Question

Isaiah Anthony · Accepted Answer

You can easily do this by inserting values in x and plotting some points.

You can graph this easily by making a table of x and y values. But first, we must find the vertex #(h,k)#. To solve for the vertex, we'll start with this formula (#h# is the value of the abscissa of the vertex.): #h=-b/(2a)# #h=-[(-5)]/[2(2)]# #h=5/4# Now to find #k# (the ordinate of the vertex), we will simply plug in #5/4# to #x#. #y=2x^2-5x-3# #y=2(5/4)^2-5(5/4)-3# #y=2(25/16)-25/4-3# #y=25/8-25/4-3# #y=25/8-50/8-3# #y=-25/8-3# #y=-25/8-24/8# #y=-49/8# The vertex is #(5/4,-49/8)#. After plotting the vertex, just plug in other values into x and graph them. Start with simple ones such as the y-intercept (set #x# to #0#). Remember that this is a quadratic equation, so your graph must be a parabola. graph{2x^2-5x-3 [-14.24, 14.24, -7.12, 7.12]}

Genesis Allen · Answer

y= (2x+1) (x-3) graph{2x^2-5x-3 [-6.07, 7.977, -6.18, 0.847]}

Cross factorise the quadratic equation to get the (2#x#+1) (#x#-3) equation. Then, put: 2#x#+1=0 so make #x# the subject of the formula #x#=#-1/2# And then, #x#-3=0 so move -3 over #x#=3 So #-1/2# and 3 are your #x#- intercepts. To find the #y#- intercept you need to complete the square, making the quadratic into the form of #a(x-h)^2# + k, so So your #y#- intercept is 1.25. (Ignore the negative! Always change it to positive) And your minimum point will be (1.25,-6.12).

Jace Anderson · Answer

undefined To graph the function $ y = 2x^2 - 5x - 3 $, you can follow these steps:

1. Plot the vertex of the parabola, which is given by the formula $ x = -\frac{b}{2a} $ for a quadratic function in the form $ y = ax^2 + bx + c $.
2. Calculate the y-coordinate of the vertex by substituting the x-coordinate into the function.
3. Determine the direction of the parabola by checking the coefficient of the $ x^2 $ term (if it's positive, the parabola opens upwards; if it's negative, it opens downwards).
4. Plot additional points by choosing x-values and substituting them into the equation to find the corresponding y-values.
5. Connect the plotted points smoothly to form the graph of the parabola.