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Start by identifying a, b, and c.
We want to draw the graph of a quadratic function written in standard form. y=ax^2+bx+c To do so, we will follow five steps.
Let's do it!
y=3x^2-4x+1 ⇕ y= 3x^2+( - 4)x+ 1 We have identified that a= 3, b= - 4, and c= 1.
x= 2/3
(a/b)^m=a^m/b^m
a*b/c= a* b/c
a/b=.a /3./.b /3.
Rewrite 1 as 3/3
Add and subtract fractions
Because in our equation we have that c=1, the y-intercept is 1. Let's plot this point and the point symmetric across the axis of symmetry.
Since a=3, which is greater than zero, we know that our parabola opens upwards. Let's draw a smooth curve connecting the three points we have. We should not use a straight edge for this!
One common mistake when identifying the key features of a parabola algebraically is forgetting to include the negative signs in the values of the constants. The standard form is addition only, so any subtraction must be treated as negative values of a, b, or c. Let's look at an example. y=3x^2-4x-2 ⇕ y= 3x^2+( -4x)+( -2) In this case, the values of a, b, and c are 3, -4, and -2. They are not 3, 4, and 2. cccc a=3, & b= 4, & c= 2 & * a= 3, & b= -4, & c= -2 & ✓