Because the question specifies a function, we must discard the form that is not a function:
#x = ay^2+by+c#
and use only the form:
#y = ax^2+bx+c" [1]"#
Using the point #(0,3)#, we substitute 0 for x and 3 for y into equation [1] and the solve for c:
#3 = a(0)^2+b(0)+c#
#c=3#
Substitute 3 for c into equation [1]:
#y = ax^2+bx+3" [1.1]"#
Using the point #(1,-4)# we substitute 1 for x and -4 for y into equation [1.1] to obtain an equation that contains "a" and "b" as variables:
#-4 = a(1)^2+b(1)+3#
#a + b = -7" [2]"#
We do the same thing using the point #(2,-9)#
#-9 = a(2)^2+b(2)+3#
#4a+2b = -12" [3]"#
Write equations [2] and [3] together as a system of equations:
#a + b = -7" [2]"#
#4a+2b = -12" [3]"#
Multiply both sides of equation [2] by -2 and add the results to equation [3]:
#4a-2a +2b-2b = -12+14#
This makes the terms containing "b" become 0:
#2a = 2#
#a = 1#
Substitute 1 for "a" into equation [2] and then solve for "b":
#1 + b = -7#
#b = -8#
Substitute 1 for "a" and -8 for "b" into equation [1.1]:
#y = x^2-8x+3" [1.2]"#
Here is a graph of the 3 points and equation [1.2]:
Quadratic Function Calculator is a free online tool that displays the graph of the quadratic function. BYJU’S online quadratic function calculator tools make the calculation faster and it displays the graph in a fraction of seconds.
How to Use the Quadratic Function Calculator?
The procedure to use the quadratic function calculator is as follows:
Step 1: Enter the quadratic equation in the input field
Step 2: Now click
the button “Plot Graph” to get the graph
Step 3: Finally, the graph of the quadratic function will be displayed in the new window
What is Meant by the Quadratic Function?
In mathematics, the quadratic function is a function which is of the form f(x) = ax2 + bx+c, where a, b, and c are the real numbers and a is not equal to zero. When the quadratic function is plotted in a graph, the curve obtained should be a parabola. The parabola is a “U-Shaped Curve”. The parabola obtained may be facing upward or downward depending on the coefficient sign of “a”, but it may have a difference in their width or the steepness.
This calculator finds the equation of parabola with vertical axis given three points on the graph of the parabola. Also
Find Equation of Parabola Passing Through three Points - Step by Step Solver.
This calculator is based on solving a system of three equations in three variables
How to Use the Calculator
1 - Enter the x and y coordinates of three points A, B and C and press "enter". Two equations are displayed: an exact one (top one) where the coefficients are in fractional forms an the second with approximated coefficients whose number of decimal number of decimal places may be chosen.When at least two points are on a vertical line (x coordinate of A equals the x coordinate of B for example), no equation is found for a parabola with vertical axis. Numbers may be entered in decimal (example: 1.02) or fractional (example: 4/5) forms.
| |||||
| |||||
| |||||
| |||||
| |||||
Enter your function here. How shall your function be transformed? By in x-direction By in y-direction By to the By to the | |||||
Degree of the function:
( The degree is the highest power of an x. ) Symmetries: y-axis intercept Roots / Maxima / Minima /Inflection points: Characteristic points: Slope at given x-coordinates: |
What are quadratic functions?
Quadratic functions are functions of the form . This means, there is no x to a higher power than . The graph of a quadratic function is a parabola.