State the vertex, direction of opening, axis of symmetry, y intercept, and maximum or minimum value for each of the following:

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State the vertex, direction of opening, axis of symmetry, y intercept, and maximum or minimum value for each of the following:

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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\[y=(x+4)^{2}+1\]
expand the right hand side \[y = x^2 +8x + 17\] the coefficient of x^2 determines concavity.... +ve concave up -ve concave down the parabola is concave up x = -b/2a gives the line of symmetry of the parabola.... (-b/2a comes from the general quadratic formula) so x = -8/(2 x 1) the line of symmetry is x = -4 as the parabola is concave up it will have a minimum... The vertex is on the line x = -4 so substitute into the equation to find the coordinates of the vertex... (-4, 1) the y value from the above is the minimum value... to find the y- intercept, let x = 0 and solve.... intercept y = 17

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