How do you graph the quadratic function and identify the vertex and axis of symmetry for $y = - x^{2} + 4 x - 2$ $y=-x^2+4x-2$ ?

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How do you graph the quadratic function and identify the vertex and axis of symmetry for $y = - x^{2} + 4 x - 2$ $y=-x^2+4x-2$ ?

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Answer 1 · 2017-03-21T13:59:12

Vertex $\to (x, y) = (2, 2)$ $->(x,y)=(2,2)$
Axis of symmetry $\to x = 2$ $->x=2$

Explanation:

As the $x^{2}$ $x^2$ part is negative the graph is of general shape $\cap$ $nn$

The axis of symmetry coincides with $x_{vertex}$ $x_("vertex")$

$Determine the vertex and axis of symmetry$ $color(blue)("Determine the vertex and axis of symmetry")$

Write as $y = - 1 (x - 4 x) - 2$ $y=-1(xcolor(red)(-4)x)-2$

$Axis of symmetry = x_{vertex} = (- \frac{1}{2}) \times (- 4) = + 2$ $"Axis of symmetry "=x_("vertex")=(-1/2)xx(color(red)(-4)) = +2$

By substitution:

$y_{vertex} = - {(2)}^{2} + 4 (2) - 2 = + 2$ $y_("vertex")=-(2)^2+4(2)-2 = +2$

Vertex $\to (x, y) = (2, 2)$ $->(x,y)=(2,2)$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$Determine the y-intercept$ $color(blue)("Determine the y-intercept")$

Consider the given equation: $= - x^{2} + 4 x - 2$ $" "=-x^2+4xcolor(magenta)(-2)$

$y_{intercept} = - 2$ $y_("intercept")=color(magenta)(-2)$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$Determine the x-intercept$ $color(blue)("Determine the x-intercept")$

Using $y = a x^{2} + b x + c where x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ $y=ax^2+bx+c" where "x=(-b+-sqrt(b^2-4ac))/(2a)$

$a = - 1; b = + 4; c = - 2$ $a=-1"; "b=+4"; "c=-2$

$x = \frac{- 4 \pm \sqrt{{(4)}^{2} - 4 (- 1) (- 2)}}{2 (- 1)}$ $x=(-4+-sqrt((4)^2-4(-1)(-2)))/(2(-1))$

I will let you finish this bit.

Tony B Tony B

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How do you graph the quadratic function and identify the vertex and axis of symmetry for $y = - x^{2} + 4 x - 2$ $y=-x^2+4x-2$ ?

1 Answer

Explanation:

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Science

Math

Humanities

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How do you graph the quadratic function and identify the vertex and axis of symmetry for y=-x^2+4x-2y=−x2+4x−2y=-x^2+4x-2?

1 Answer

Explanation:

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How do you graph the quadratic function and identify the vertex and axis of symmetry for $y = - x^{2} + 4 x - 2$ $y=-x^2+4x-2$ ?