Answer:
y = (x - 4)(x + 1)
; zeroes at (-1, 0) and (4, 0)
minimum at (3/2, -25/4); axis of symmetry at x = 3/2
Step-by-step explanation:
Your equation is: y = x² - 3x - 4
1. Factor the quadratic
x² - 3x - 4 = (x - 4)(x + 1)
2. Solve the quadratic
x - 4 = 0 x + 1 = 0
x = 4 x = -1
The zeroes are at (-1, 0) and (4, 0).
3. Find the vertex
The standard form for the equation of a parabola is
y = ax² + bx + c
Your equation is
y = x² - 3x - 4
a = 1, b = -3, c = -4
The vertex form of a parabola is
y = a(x - h)² + k
where (h, k) is the vertex of the parabola.
h = -b/(2a) and k = f(h)
a is positive, so the parabola opens upward, and the vertex is a minimum.
h = -(-3)/(2×1)
= 3/2
k = 1(3/2)² - 3(3/2) - 4
= 9/4 - 9/2 - 4
= (9 - 18 - 16)/4
= -25/4
h = 3/2; k = -25/4
The vertex is at (3/2, -25/4).
The axis of symmetry is a vertical line passing through the vertex at x = 3/2.
The Figure below shows that your equation us an upward pointing parabola with zeroes at (-1,0) and (4, 0), vertex at (1.5, -6.25), and axis of symmetry at x = 1.5.
