Find the quadratic function y = a(x-h)^2whose graph passes through the given points (6, -1) and (4, 0). a) y = 1/4(x-5)^2 b) y = 1/4(x-5)^2 c) y = -1/4(x-6)^2 d) y = 1/4(x-6)^2

Answer: -1/2x - 2.

Step-by-step explanation:

To find the quadratic function y = a(x-h) that passes through the points (6, -1) and (4, 0), we can substitute the given points into the equation and solve for a and h. Let's go through the steps:

1. Substitute the coordinates of the first point (6, -1) into the equation:

-1 = a(6 - h)

2. Substitute the coordinates of the second point (4, 0) into the equation:

0 = a(4 - h)

3. Now we have a system of two equations with two unknowns. We can solve this system to find the values of a and h.

From the equation -1 = a(6 - h), we can rewrite it as:

-a(6 - h) = 1

From the equation 0 = a(4 - h), we can rewrite it as:

-a(4 - h) = 0

4. Simplifying the equations, we get:

-6a + ah = 1 (equation 1)

-4a + ah = 0 (equation 2)

5. Subtracting equation 2 from equation 1 eliminates the ah term:

-6a + ah - (-4a + ah) = 1 - 0

-6a + ah + 4a - ah = 1

-2a = 1

6. Solving for a, we divide both sides by -2:

a = -1/2

7. Substitute the value of a back into either equation (let's use equation 2) to solve for h:

-4(-1/2) + h(-1/2) = 0

2 + h/2 = 0

h/2 = -2

h = -4

8. Now we have the values of a = -1/2 and h = -4. We can substitute these values back into the original equation y = a(x-h) to find the quadratic function:

y = -1/2(x - (-4))

y = -1/2(x + 4)

y = -1/2x - 2

Therefore, the quadratic function that passes through the points (6, -1) and (4, 0) is

AI-generated answer

To find the quadratic function y = a(x-h) that passes through the points (6, -1) and (4, 0), we can substitute the given points into the equation and solve for a and h. Let's go through the steps:

1. Substitute the coordinates of the first point (6, -1) into the equation:

-1 = a(6 - h)

2. Substitute the coordinates of the second point (4, 0) into the equation:

0 = a(4 - h)

3. Now we have a system of two equations with two unknowns. We can solve this system to find the values of a and h.

From the equation -1 = a(6 - h), we can rewrite it as:

-a(6 - h) = 1

From the equation 0 = a(4 - h), we can rewrite it as:

-a(4 - h) = 0

4. Simplifying the equations, we get:

-6a + ah = 1 (equation 1)

-4a + ah = 0 (equation 2)

5. Subtracting equation 2 from equation 1 eliminates the ah term:

-6a + ah - (-4a + ah) = 1 - 0

-6a + ah + 4a - ah = 1

-2a = 1

6. Solving for a, we divide both sides by -2:

a = -1/2

7. Substitute the value of a back into either equation (let's use equation 2) to solve for h:

-4(-1/2) + h(-1/2) = 0

2 + h/2 = 0

h/2 = -2

h = -4

8. Now we have the values of a = -1/2 and h = -4. We can substitute these values back into the original equation y = a(x-h) to find the quadratic function:

y = -1/2(x - (-4))

y = -1/2(x + 4)

y = -1/2x - 2

Therefore, the quadratic function that passes through the points (6, -1) and (4, 0) is y = -1/2x - 2.