Quadratics
Standard Form
Summary of standard form.
a value tells us the direction of opening. If a value is negative parabola opens downwards and if a is positive parabola opens upwards.
Quadratic formula ( in the following picture )
Completing the square help us to find Vertex and change standard to vertex form.
Today I show you the basics of Standard form like How to convert standard to vertex form.
Standard form
y = ax² + bx + c
What does a tells us about.
How to find Vertex by using completing the square and; convert standard to vertex form.
y = (3x² + 6x) - 10
y = 3(x² + 2x) - 10 { Take out 3 }
y = 3(x² + 2x +1 -1) - 10 { When you divide 2/2 and then square you get 1}
y = 3(x² +2x +1) -3 -10 {Multiply 3 by -1 you get -3 and take it out }
y = 3(x² +2x +1) - 13
y = (x + 1)² - 13 { Now this is vertex form so the vertex is ( - 13, -1)
AND YOU ALSO SEE HERE HOW WE CONVERT STANDARD FORM TO VERTEX FORM.
Quadratic formula Example to find x intecepts.
Discriminant
D=b^2-4(a)(c)
a=2
b=6
c=12
D=b^2-4(a)(c)
D=6^2 - 4(2)(12)
D=36-96
D= -60
So, If the 'D' value is less than '0', than there will be no x-intercepts.
If the 'D' value is '0' than there will be 1 x-intercept.
If the 'D' value is greater than '0', than there will be 2 x-intercepts.
Video for word problem ; how to solve by completing the square and as well as about revenue.
Word problem about how to find Rectangle dimensions.
Word problem about consecutive integers.
Learning goals
2. Today I also learn about completing the square.