A quadratic function has its vertex at the point \( (-5,-4) \). The function passes through the point \( (8,-3) \). When written in vertex form, the function is \( f(x)=a(x-h)^{2}+k \), where: \( a= \) \( h= \) \( k= \)
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To write the quadratic function in vertex form, we first identify the vertex coordinates: \( h = -5 \) and \( k = -4 \). This means our function starts as \( f(x) = a(x + 5)^2 - 4 \). Next, we use the point \( (8, -3) \) to find the value of \( a \). Plugging in \( x = 8 \) and \( f(x) = -3 \): \[ -3 = a(8 + 5)^2 - 4 \] \[ -3 = a(13)^2 - 4 \] \[ -3 = 169a - 4 \] \[ 1 = 169a \] \[ a = \frac{1}{169} \] So the quadratic function in vertex form is: \[ f(x) = \frac{1}{169}(x + 5)^2 - 4 \] In summary: \( a = \frac{1}{169} \) \( h = -5 \) \( k = -4 \)
