# f(x)=3(x-1)^2-3 in need vertex axis of symmetry x intercepts showing work how to get the answers?

in need vertex axis of symmetry x intercepts with showing work how to get the answers

Relevance

Vertex form: y = a(x - h)^2 + k, where (h, k) is the vertex and x = h is the equation of the axis of symmetry

The vertex of this function is (1, -3) and the equation of the axis of symmetry is x = 1. To find the x-intercepts, substitute 0 for f(x) and solve for x:

0 = 3(x - 1)^2 - 3

3 = 3(x - 1)^2

1 = (x - 1)^2

±1 = x - 1

x - 1 = 1 or x - 1 = -1

x = 2 or x = 0

The x-intercepts are 2 and 0 or (2, 0) and (0, 0).

• f(x)=3(x-1)^2-3

is the standard vertex form of a parabolic equation with a vertical axis.

y = a(x-g)² + h

with vertex, (x,y) = (g, h)

The vertex can be read directly from the equation, (x, y) = (1, -3)

Axis of symmetry is the vertical line through the vertex, x = 1

For the x-intercepts, set y = 0 and solve for x:

3(x-1)² - 3 = 0

x² - 2x + 1 - 1 = 0

x² - 2x = 0

x(x-2) = 0

x = 0, 2

the x-intercepts are (0, 0) and (2, 0)

• read the vertex from the equation, when y = a(x - h)² + k, vertex is (h,k), so

vertex is (1, -3)

which means axis of symmetry is x = 1

for x intercepts, solve

3(x - 1)² - 3 = 0

3(x - 1)² = 3

(x - 1)² = 1

x - 1 = ±1

x = 1 + 1 = 2 ........... or x = 1 - 1 = 0

• Vertex may well be discovered by skill of way of the formulation x=-b/2a for the final quadratic equation of the type ax^2+bx+c. for this reason vertex=-2/(2*a million)=-a million And for the y coordinate, we take f(-a million)=-a million. The x intercept we are in a position to discover by skill of way of factoring; x^2+2x = x(x+2); so x = 0, -2. The function is a polynomial, for this reason it incredibly is non-stop on the set of genuine numbers and is defined for all x. area = -infinity, infinity. the form is the set of all form such that y is extra effective than or equivalent to -a million.

• Anonymous

✐Explanation✐

Vertex:

Recall that:

y = a(x - h)² + k

in which...

(h,k) is a vertex.

Indicate the vertex; you get (1, -3).

x-intercept:

Make f(x) = 0.

0 = 3(x - 1)² - 3

Solve for x.

0 = 3(x² - 2x + 1) - 3

0 = 3x² - 6x + 3 - 3

0 = 3x² - 6x

0 = 3x(x - 2)

x = {0, 2}