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What is the axis of symmetry and vertex for the graph #y =-2x^2-3x+4#?

Answer 1

Eva Abramson

Axis of symmetry: #x=-3/4#
Vertex at #(-3/4, 41/8)#

Solution is by Completing the Square

#y=-2x^2-3x+4#

#y=-2(x^2+3/2x)+4#

#y=-2(x^2+3/2x+9/16-9/16)+4#

#y=-2((x+3/4)^2-9/16)+4#

#y=-2(x+3/4)^2+9/8+4#

#y-41/8=-2(x+3/4)^2#

#-1/2(y-41/8)=(x--3/4)^2#

Axis of symmetry: #x=-3/4# Vertex at #(-3/4, 41/8)#

graph{y=-2x^2-3x+4[-20,20,-10,10]}

God bless....I hope the explanation is useful.

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Answer 2

Jameson Allen

The axis of symmetry for the graph y = -2x^2 - 3x + 4 is x = -3/(-4). The vertex of the parabola is located at the point (-3/(-4), f(-3/(-4))), where f(x) is the function. Therefore, the vertex is at the point (3/4, 31/8).

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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.