The graph of a quadratic function f(x) has a minimum at (2,3) and passes through the point (2,13). The function g(x) is represented by the equation g(x) = (x + 2)(x  3).
How much greater is the yintercept of g(x) than f(x)?
For f(x):
the vertex is (2,3) and it passes through (2,13) substitute that information into vertex form f(x) = a(x  h)² + k {vertex form of a quadratic function} 13 = a[2  (2)]²  3 {substituted point and vertex into vertex form} 13 = a(4)²  3 {worked inside parentheses} 13 = 16a  3 {evaluated exponent} 16 = 16a {added 3 to each side} a = 1 {divided each side by 16} f(x) = 1[x  (2)]²  3 {substituted vertex and value of a back into vertex form} f(x) = (x + 2)²  3 {simplified} = (x + 2)(x + 2)  3 {began transforming into standard form} = x² + 4x + 4  3 {squared the binomial} f(x) = x² + 4x + 1 {combined like terms} yintercept of f(x) is 1 For g(x): g(x) = (x + 2)(x  3) = (x²  x  6) {used FOIL method / distributive property} g(x) = x² + x + 6 {distributed negative sign} yintercept of g(x) is 6 The yintercept of g(x) is 5 greater than the yintercept of f(x). Ask Algebra House Comments are closed.

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