# How do you find the vertex and the intercepts for #y = 1/4x^2 + 1/ 2x - 3/4#?

Vertex is at

and y intercept is at

graph{1/4x^2+1/2x-3/4 [-10, 10, -5, 5]}

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Alternative approach

Vertex

Given:

Compare to the form of

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You have three methods:

- Using the completed square form equation you can read it directly off but with a small amount of adjustment.

Complete breakdown on this can be found on https://tutor.hix.ai2.factorising or use the formula to determine the

#x# intercepts and the#x# value of the vertex will be half way between- You can do it this way:

Note that this process is part of that for completing the square.Write as:

#y=1/4(x^2color(red)(+2x))-3/4# #x_("vertex") = (-1/2)xx(color(red)(+2)) = -1# Buy substitution

#y_("vertex")=1/4(-1)^2+1/2(-1)-3/4 = -1# Vertex

#->(x,y)=(-1,-1)#

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#color(blue)("Determine the "x_("interpts")# Using other method

#y=ax^2+bx+c =0color(white)(..)# where#x=(-b+-sqrt(b^2-4ac))/(2a)# #a=1/4; b=1/2; c= -3/4# #x=(-1/2+-sqrt((1/2)^2-4(1/4)(-3/4)))/(2xx1/4)# #x=-1+-2sqrt( 1/4+3/4)# #x=-1+-2# #x=-3 and x=1#

- You can do it this way:

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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.

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.

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.

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