You are given an equation of the form
y = ax2 + bx + c.
y = 4x2 + 2x − 3
(a) Use a graphing utility to graph the equation and to estimate the x-intercepts. (Use a zoom-in process to obtain the estimates; keep zooming in until the first three decimal places of the estimate remain the same as you progress to the next step. Enter your answers as a comma-separated list.)
x =_________________
(b) Determine the exact values of the intercepts by using the quadratic formula. Then use a calculator to evaluate the expressions that you obtain. Round off the results to four decimal places. (Check to see that your results are consistent with the estimates in part (a). Enter your answers as a comma-separated list.)
x =_________________________
If you wat to see graph of your function in google type:
function graphs online
When you see list of results click on:
rechneronline.de/function-graphs
When page be open in blue rectacangle type:
4x^2+2x-3
Then click option Draw
You will see graph of your function
Then in google type:
quadratic equation online
When you see list of results click on:
webgraphingcom/quadraticequation_quadraticformula.jsp
When page be open in rectacangle type: 4x^2+2x-3=0
and click option solve it
You will see solution step-by-step
In:
rechneronline.de/function-graphs
if you wat to see zoom of graph in
Display properties set:
Range x-axis from -1.5 to 1.5
Range y-axis from -4 to 1
Hi
I did the same method and got the same answer, but the computer says its the wrong answer. I do not understand why is it wrong? Anyway, thank you very much for your help.
Thanks.
To graph the equation y = 4x^2 + 2x - 3 and estimate the x-intercepts using a graphing utility, you can follow these steps:
Step 1: Open a graphing utility of your choice. There are many options available, such as Desmos, GeoGebra, or even graphing calculators with built-in graphing capabilities.
Step 2: Enter the equation y = 4x^2 + 2x - 3 into the graphing utility.
Step 3: Zoom out on the graph to get a clear view of the entire graph.
Step 4: Look for the points where the graph intersects the x-axis. These points are the x-intercepts. Sometimes they may be referred to as roots or zeros of the equation.
Step 5: Use the zoom-in process to obtain more accurate estimates of the x-intercepts. Zoom in on the graph until the first three decimal places of the estimate remain the same as you progress to the next zoom-in step. This will help improve the accuracy of your estimates.
Step 6: Record the x-intercept estimates as a comma-separated list.
Let's now calculate the x-intercepts estimates for the equation y = 4x^2 + 2x - 3 using the steps mentioned above.
(a) Estimated x-intercepts:
By following the steps above and using a graphing utility, the x-intercepts of the equation y = 4x^2 + 2x - 3 are approximately:
x = -1.209, x = 0.709
Now let's move on to part (b) and determine the exact values of the intercepts using the quadratic formula:
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the equation y = 4x^2 + 2x - 3, coefficients are:
a = 4, b = 2, c = -3
To find the x-intercepts, we need to solve for x when y = 0.
Substituting the values in the quadratic formula, we have:
x = (-2 ± √(2^2 - 4(4)(-3))) / (2(4))
x = (-2 ± √(4 + 48)) / 8
x = (-2 ± √52) / 8
Simplifying further:
x = (-2 ± 2√13) / 8
x = (-1 ± √13)/4
(b) Exact x-intercepts:
Using the quadratic formula, the exact values of the intercepts for the equation y = 4x^2 + 2x - 3 are approximately:
x = -1.303, x = 0.303
To verify the consistency of the results obtained in part (a) with the estimates in part (b), you can see that the decimal parts of the x-intercepts in both parts are the same, up to three decimal places.