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

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Answer 1 · 2016-10-17T11:01:24

See explanation

Consider the standard form of $y=ax^2+bx+c$

The y-axis intercept is the constant c which in this case gives $y=3$

As the $bx$ term is not 0 (not there) then the graph is symmetrical about the y-axis. Consequently the vertex is actually on the y-axis.

$color(blue)("Axis of symmetry is: "x=0)$
$color(blue)("Vertex "->(x,y)=(0,3)$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$color(brown)("Foot Note:")$

As the $ax^2$ term is negative the graph form is $nn$

If the $ax^2$ term had been positive then in that instance the graph form would be $uu$

As a general rule the axis of symmetry is at $x=(-1/2)xxb/a$

Consider the example of $y=ax^2+bx+c" "->" "y=-2x^2+3x-4$

In this case the axis of symmetry will be at:

$x=(-1/2)xxb/a" "->" "(-1/2)xx3/(-2)" " =" " 3/4$

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