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What is the the vertex of #y = 3x^2-2x+4 #?

Answer 1

Convert into vertex form to get
vertex at #(1/3,3 2/3)#

General vertex form: #color(white)("XXX")color(green)(y=m(x-a)^2+b)# with vertex at #(color(green)(a, b))#

Given #color(white)("XXX")y=3x^2-2x+4#

Extract #m# from terms including #x# #color(white)("XXX")y=3(x^2-2/3x)+4#

Complete the square #color(white)("XXX")y=color(red)(3)(x^2-2/3xcolor(blue)(+(1/3)^2))+4-color(red)(3)*color(blue)((1/3)^2)#

Re-write as a squared binomial and simplify the numeric expression #color(white)("XXX")y=3(x-1/3)^2+3 2/3# which is the desired "vertex form" graph{3x^2-2x+4 [-1.07, 2.775, 2.868, 4.788]}

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Answer 2

Avery Alexander

The vertex of the quadratic function y = 3x^2 - 2x + 4 is at the point (h, k), where h = -b/(2a) and k = f(h), and a, b, and c are coefficients of the quadratic equation ax^2 + bx + c. In this equation, a = 3, b = -2, and c = 4. Plug these values into the formulas to find the vertex.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.