Y = ax² + bx + c ⇒ y = f(x)
f(x) = ax² + bx + cGiven: x² - 12y + 5 = 0
Convert to y = ax² + bx + c
x² - 12y + 5 = 0
x² + 5 = 12y
12y = x² + 5
12y/12 = x²/12 + 5/12
y = A.) Set y to = 0 Solve for roots (zeroes) using the method extracting the square roots.
Use this method when b = 0 in equation ax² + bx + c = 0.
x² + 5 = 0
x² = -5
x₂ = THE ZEROES (ROOTS) are and .
It means that the equation has no real roots, and the graph (parabola) that opens upward is above the x-axis.
B.) Find the vertex of the parabola.
Since the equation has a positive leading leading term (
), the parabola opens upward (u-shaped), and the vertex is the minimum.Vertex = (h, k)
h = h = 0
k = f(h)
Plug -in the value of h (0) to x in equation
k = 0 + ⁵/₁₂k = ⁵/₁₂
Vertex = (h, k)Vertex = (0, ⁵/₁₂) FINAL ANSWER: The vertex is (0, ⁵/₁₂) and the zeroes (roots) are and .
Please click image to see the graph of the given equation.