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Put the quadratic into vertex form and state the coordinates of the vertex.

y=x^(2)+2x-24
Vertex Form:
y=
Vertex:
(◻,◻)

Put the quadratic into vertex form and state the coordinates of the vertex. $\newline$ $y=x^{2}+2 x-24$ $\newline$ Vertex Form: $y=$ $\newline$ Vertex: $(\square, \square)$

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Convert equations of parabolas from general to vertex form

Full solution

Q. Put the quadratic into vertex form and state the coordinates of the vertex.

\newline

y=x^{2}+2 x-24

\newline

Vertex Form:

y=

\newline

Vertex:

(\square, \square)

Identify Vertex Form: Identify the vertex form of a parabola. $\newline$ The vertex form of a parabola is $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
Complete the Square: Complete the square for the quadratic equation $y = x^2 + 2x - 24$ . $\newline$ To complete the square, we need to find a value that, when added and subtracted to the equation, forms a perfect square trinomial with the $x^2$ and $2x$ terms.
Calculate Value: Calculate the value needed to complete the square. $\newline$ The coefficient of $x$ is $2$ , so we take half of it, which is $1$ , and then square it to get $1^2 = 1$ .
Add and Subtract: Add and subtract the calculated value inside the equation. $\newline$ We add $1$ and subtract $1$ inside the parentheses to maintain the equality of the equation. $\newline$ $y = x^2 + 2x + 1 - 1 - 24$
Rewrite Equation: Rewrite the equation by grouping the perfect square trinomial and the constants. $\newline$ $y = (x^2 + 2x + 1) - 25$
Factor Trinomial: Factor the perfect square trinomial. $\newline$ $y = (x + 1)^2 - 25$
Write in Vertex Form: Write the equation in vertex form. $\newline$ The vertex form of the equation is $y = (x + 1)^2 - 25$ .
Identify Vertex Coordinates: Identify the coordinates of the vertex. The vertex form $y = a(x - h)^2 + k$ gives us the vertex $(h, k)$ . In our equation $y = (x + 1)^2 - 25$ , we have $h = -1$ and $k = -25$ . Therefore, the vertex is $(-1, -25)$ .

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