Introduction: Graphing Quadratics and Vertex Form Summative
The y-intercept in the equation is always the constant in the end of the equation.
Step 1: First Way to Find the X-intercepts (Roots, Solutions, Zeros): the Quadratic Formula
First Step: In the first step you put the numbers in your equation into a=... and b=.... and c=... The coefficient of x squared is a, the coefficient of x is b, and the constant is c. The second step is you put in the numbers in the quadratic formula then you solve for x using the formula, you solve the numbers under the roots first by multiplying 4 and a and c. Then you add the number you get with what you squared and take out its square root. Then you continue solving for x and eventually you will get two answers and these two answers are the x-intercepts.
Step 2: Second Way to Find the X-intercepts (Roots, Solutions, Zeros): Factoring
First you multiply the first number (the first coefficient) by the last number (the constant), which will get you 9. Then you will find two number that when you multiply them will get you nine and when added will get you the number that's the coefficient of x which is 8. The numbers are 9 and 1. Then you factorize by taking out the greatest common factor and in the end you will end up with your x-intercepts which are x=1/3 and x=-3.
Step 3: How to Find the Axis of Symmetry:
The formula for finding the axis of symmetry is -b/2a so you do the same thing, the coefficient of x squared is a, the coefficient of x is b, and the constant is c. Then you put the numbers in for the letters in the axis of symmetry formula. Eventually you will get a number which in this equation is -1.33.
Step 4: How to Find the Vertex of a Quadratic From Standard Form:
The formula for finding the axis of symmetry is -b/2a so you do the same thing, the coefficient of x squared is a, the coefficient of x is b, and the constant is c. Then you put the numbers in for the letters in the axis of symmetry formula. Eventually you will get a number which in this equation is -1.33, you will then put this number in for x in the equation so it will be 3(-1.33)^2 + 8(-1.33) - 3 and then you solve it. You will then get a number which in this situation is -8.33. Then you will put the axis of symmetry as your first point and the number you got after plugging the axis of symmetry in as your second point, so your vertex will be (-1.33,-8.33).
Step 5: How to Graph the Quadratic Equation:
Fist you draw a graph and then you take all the points we got from the previous instructions and you put them on the graph. So you put the axis of symmetry first, then the x intercepts, then the vertex, and lastly the y intercept. Then you graph by connecting these points preferably starting from the x intercept and you have to go through the y intercept while connecting the points.
Step 6: How to Find the Vertex Form:
The formula of vertex form is y=a(x-h)^2+k, so firstly you take the points from the vertex and you plug in the x in for h and you flip its sign, and the y for the k. Then you take the other point on the parabola and you plug in the x for the x and the y for the y. Then you solve the equation for a by solving what's in the brackets and you square it then you add the numbers and take it on the other side. Then eventually you will have the a and with it you put it in for the a but then you remove the other points on the parabola, This will leave you with y=-20(x-1)^2-4.
Step 7: How to Find Standard Form From Vertex Form:
First you take the numbers in the brackets which is (x-1)^2 and you turn it into a trinomial which will get you (x^2-2x+1). Then you put the a outside the brackets which will make it y= -20(x^2-2x+1) then you distribute the number. Which will then equal -20x^2-40x-20 then you add the constant add the end of the vertex form equation which is -4 to the constant which in this situation is -20 so you will end up with -20x^2-40x-24 as your standard form.