The equation of a parabola is y = x^2 + 8x + 21. Write the equation in vertex form. Write any numbers as integers or simplified proper or improper fractions. ______

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The equation of a parabola is y = x^2 + 8x + 21. Write the equation in vertex form.  Write any numbers as integers or simplified proper or improper fractions. ______

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Identify vertex form: Identify the vertex form of a parabola. The vertex form of a parabola is given by the equation y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.Complete the square: Complete the square to rewrite the given equation in vertex form. We start with the given equation y = x^2 + 8x + 21. To complete the square, we need to find the value that makes x^2 + 8x a perfect square trinomial. We do this by taking half of the coefficient of x, squaring it, and adding it to and subtracting it from the equation. The coefficient of x is 8, so half of 8 is 4, and 4 squared is 16. We add and subtract 16 to the equation.Add and subtract: Add and subtract 16 to the equation. y = x^2 + 8x + 16 + 21 - 16 Now we have the perfect square trinomial x^2 + 8x + 16 and the constants 21 and -16.Factor and simplify: Factor the perfect square trinomial and simplify the constants. y = (x + 4)^2 + 21 - 16 y = (x + 4)^2 + 5 Now the equation is in vertex form, where (h, k) = (-4, 5).

The equation of a parabola is $y = x^2 + 8x + 21$ . Write the equation in vertex form. $\newline$ Write any numbers as integers or simplified proper or improper fractions. $\newline$ ______

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The equation of a parabola is y=x2+8x+21y = x^2 + 8x + 21y=x2+8x+21. Write the equation in vertex form.\newlineWrite any numbers as integers or simplified proper or improper fractions.\newline______

The equation of a parabola is $y = x^2 + 8x + 21$ . Write the equation in vertex form. $\newline$ Write any numbers as integers or simplified proper or improper fractions. $\newline$ ______