The equation of a parabola is y = x^2 - 8x + 24. Write the equation in vertex form. Write any numbers as integers or simplified proper or improper fractions. ______

Identify Vertex Form: Identify the vertex form of a parabola, which is y = a(x - h)^2 + k.Calculate and Adjust: Start with the given equation y = x^2 - 8x + 24. To complete the square, calculate (8/2)^2 = 4^2 = 16, then add and subtract 16 inside the equation.Rewrite Equation: Rewrite the equation as y = x^2 - 8x + 16 + 24 - 16.Group and Combine: Group the perfect square trinomial and combine the constants: y = (x^2 - 8x + 16) + (24 - 16).Simplify Constants: Simplify the constants: y = (x^2 - 8x + 16) + 8.Factor Trinomial: Factor the perfect square trinomial: y = (x - 4)^2 + 8.

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The equation of a parabola is $y = x^2 - 8x + 24$ . Write the equation in vertex form. $\newline$ Write any numbers as integers or simplified proper or improper fractions. $\newline$ ______

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Algebra 1

Write a quadratic function in vertex form

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Q. The equation of a parabola is

y = x^2 - 8x + 24

. Write the equation in vertex form.

\newline

Write any numbers as integers or simplified proper or improper fractions.

\newline

______

Identify Vertex Form: Identify the vertex form of a parabola, which is $y = a(x - h)^2 + k$ .
Calculate and Adjust: Start with the given equation $y = x^2 - 8x + 24$ . $\newline$ To complete the square, calculate $(8/2)^2 = 4^2 = 16$ , then add and subtract $16$ inside the equation.
Rewrite Equation: Rewrite the equation as $y = x^2 - 8x + 16 + 24 - 16$ .
Group and Combine: Group the perfect square trinomial and combine the constants: $y = (x^2 - 8x + 16) + (24 - 16)$ .
Simplify Constants: Simplify the constants: $y = (x^2 - 8x + 16) + 8$ .
Factor Trinomial: Factor the perfect square trinomial: $y = (x - 4)^2 + 8$ .