Final answer:
To find the quadratic equation in vertex form with a given vertex and a point, we use the vertex form equation (y = a(x - h)^2 + k) and substitute the vertex and point values to solve for 'a'. The correct equation, based on the provided vertex (-4, 6) and point (-5, 4), is y = -2(x + 4)^2 + 6, which is not listed among the provided options.
Step-by-step explanation:
The question asks to write the equation of a quadratic in vertex form, where the vertex is given as (-4, 6), and the quadratic passes through the point (-5, 4). A quadratic equation in vertex form is written as y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. Given the vertex (-4, 6), we substitute h = -4 and k = 6 into the vertex form, which yields y = a(x + 4)^2 + 6.
To find the value of 'a', we use the point (-5, 4) which lies on the parabola. We substitute x = -5 and y = 4 into the equation:
4 = a(-5 + 4)^2 + 6
4 = a(1)^2 + 6
4 = a + 6
Now we solve for 'a':
a = 4 - 6
a = -2
Then we substitute 'a' into the vertex form of the equation:
y = -2(x + 4)^2 + 6
Therefore, none of the given options (a, b, c, or d) is correct. The correct equation in vertex form is y = -2(x + 4)^2 + 6.