graphing equations

Question

how to correctly graph y=2x2−8x+3

Answer 1

Greetings! Lets solve this shall we ?

So, we must graph the function of f(x) = 2x² - 8x + 3 by hand correct ? First we must find the vertex of this graph using the vertex formula of quadratic equations such that

Vertex = (h, k) = ( -b/2a, f(-b/2a)), where a = 2 and b = -8.

Then, (-(-8)/2(2), f(-(-8)/2(2))) = (2, f(2))

f(2) = 2(2)² - 8(2) + 3

f(2) = 2(4) - 16 + 3

f(2) = 8 - 16 + 3

f(2) = -5

Thus, the vertex is (2, -5). Then when graphing on paper, make sure you graph this point then draw a parabola passing through this point. Note: Since the leading coefficient is 2, make the parabola a bit wider than normal. Second Note: When the leading coefficient is a whole number, the parabolas stretch out (widen). When the leading coefficient is a fraction, the parabolas compress inward.

I hope this helped!