Answer:
see explanation
Step-by-step explanation:
Given a parabola in standard form
y = ax² + bx + c ( a ≠ 0 )
Then the x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
y = x² - 8x + 13 ← is in standard form
with a = 1 and b = - 8 , then
[tex]x_{vertex}[/tex] = - [tex]\frac{-8}{2}[/tex] = 4
Substitute x = 4 into the equation for corresponding value of y
y = 4² - 8(4) + 13 = 16 - 32 + 13 = - 3
Vertex = (4, - 3 )
The axis of symmetry is a vertical line passing through the vertex with equation
x = 4 ← equation of axis of symmetry
To determine direction of opening
• If a > 0 then graph opens up
• If a < 0 then graph opens down
Here a = 1, thus graph opens up
