Complete the square to re-write the quadratic function in vertex form: y=x^(2)+3x-5 Answer: y=

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Complete the square to re-write the quadratic function in vertex form:  y=x^(2)+3x-5 Answer:  y=

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Focus on x^2 and x terms: To complete the square and rewrite the quadratic function in vertex form, we first need to focus on the x^2 and x terms. The vertex form of a quadratic function is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. We will complete the square for the x^2 + 3x part of the function.Complete the square: The coefficient of x^2 is 1, which is already in the form we need. To complete the square, we take the coefficient of x, which is 3, divide it by 2, and square the result to find the constant term that will complete the square. (3/2)^2 = 2.25 or 9/4.Rewrite the equation: We add and subtract this constant term (9/4) inside the parentheses to maintain the equality of the equation. y = x^2 + 3x + 9/4 - 9/4 - 5Factor the perfect square trinomial: Now we can rewrite the equation by grouping the perfect square trinomial and combining the constants outside the parentheses. y = (x^2 + 3x + 9/4) - 9/4 - 5Combine the constants: The perfect square trinomial (x^2 + 3x + 9/4) can be factored into (x + 3/2)^2. y = (x + 3/2)^2 - 9/4 - 5Final vertex form: Next, we need to combine the constants. To combine -9/4 and -5, we need a common denominator. Since 5 is the same as 20/4, we rewrite -5 as -20/4. y = (x + 3/2)^2 - 9/4 - 20/4Now we combine the constants -9/4 and -20/4 to get -29/4. y = (x + 3/2)^2 - 29/4The quadratic function is now written in vertex form, which is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. In this case, the vertex form of the function is: y = (x + 3/2)^2 - 29/4

Complete the square to re-write the quadratic function in vertex form: $\newline$ $y=x^{2}+3 x-5$ $\newline$ Answer: $y=$

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Complete the square to re-write the quadratic function in vertex form:\newliney=x2+3x−5 y=x^{2}+3 x-5 y=x2+3x−5\newlineAnswer: y= y= y=

Complete the square to re-write the quadratic function in vertex form: $\newline$ $y=x^{2}+3 x-5$ $\newline$ Answer: $y=$