It seems you want to work with the quadratic expression \(x^2 + 18x + 32\). Here are a few things you might be interested in doing with it:
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Factoring the Expression: To factor \(x^2 + 18x + 32\), we need two numbers that multiply to 32 (the constant term) and add to 18 (the coefficient of \(x\)). Those numbers are 2 and 16. Thus, we can factor the expression as: \[ (x + 2)(x + 16) \]
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Finding the Roots: To find the roots, we can set the equation to zero: \[ x^2 + 18x + 32 = 0 \] Using the factored form: \[ (x + 2)(x + 16) = 0 \] This gives the roots: \[ x = -2 \quad \text{and} \quad x = -16 \]
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Graphing the Quadratic: The quadratic opens upwards (since the coefficient of \(x^2\) is positive) and has its vertex at the point that is halfway between the roots. The vertex can be found using the formula: \[ x = -\frac{b}{2a} = -\frac{18}{2} = -9 \] Plugging \(x = -9\) back into the expression gives the \(y\)-coordinate of the vertex: \[ y = (-9)^2 + 18(-9) + 32 = 81 - 162 + 32 = -49 \] So the vertex is at \((-9, -49)\).
If you need anything specific done with the expression, let me know!