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use the equation \\(f(x) = x^2 + 6x - 3\\), to answer parts a) through …

Question

use the equation \\(f(x) = x^2 + 6x - 3\\), to answer parts a) through g).

a) determine whether the parabola opens upward or downward.

  • the parabola opens downward.
  • the parabola opens upward.

b) find the equation of the axis of symmetry.
the axis of symmetry is .
(type an equation.)

c) find the vertex.
the vertex of the parabola \\(f(x) = x^2 + 6x - 3\\) is .
(type an ordered pair.)

d) find the y-intercept.
the y-intercept of \\(f(x) = x^2 + 6x - 3\\) is .
(type an ordered pair.)

e) find the x-intercepts.

Explanation:

Determine the direction of opening

$$ LATEXBLOCK0 $$

Find the axis of symmetry

$$ LATEXBLOCK1 $$

Find the vertex and y-intercept

$$ LATEXBLOCK2 $$

Answer:

Question a

  • The parabola opens downward.
  • The parabola opens upward. (Correct answer)

Question b

The axis of symmetry is <blank>\(x = -3\)</blank>.

Question c

The vertex of the parabola \(f(x) = x^2 + 6x - 3\) is <blank>\((-3, -12)\)</blank>.

Question d

The y-intercept of \(f(x) = x^2 + 6x - 3\) is <blank>\((0, -3)\)</blank>.