Find the formula, in standard form $y=a x^{2}+b x+c$, for a quadratic that has roots at $x=3$ and $x$ $=-7$, and has leading coefficient of 1 .
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y=
\]
Answer
Final Answer: \(y = \boxed{x^{2} + 4x - 21}\)
Step 1 ：The roots of a quadratic equation are given by the formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\). If we know the roots of the equation, we can reverse this process to find the coefficients of the quadratic. In this case, we know that the roots are \(x = 3\) and \(x = -7\), and we know that the leading coefficient \(a = 1\). We can use these facts to find the coefficients \(b\) and \(c\).
Step 2 ：The coefficients \(b\) and \(c\) are 4 and -21 respectively. Therefore, the quadratic equation in standard form is \(y = x^2 + 4x - 21\).
Step 3 ：Final Answer: \(y = \boxed{x^{2} + 4x - 21}\)
