Answer: x = 1, 7, vertex is at (4, -9)
Explanation:
To find the x-intercepts, we will factor and solve. Finding the x-intercepts is the same as finding the solutions, where f(x) = 0. -7 and -1 multiply to 7, and -7 + -1 = -8.
y = x² - 8x + 7
y = (x - 7)(x - 1)
x = 7 x = 1
Next, we can use this equation to help us find the x-value of the vertex.
Then, we will substitute this value back into the equation to solve for the y-value.
y = x² - 8x + 7
y = (4)² - 8(4) + 7
y = -9
The vertex is at (4, -9)