Let f(x)=-1/2x^2-3x+5/2

Question

Find:

(1) y-intercept


(4) x-intercepts






(2) Axis of Symmetry



(3) Vertex

Answer 1

y = (-1/2)x² - 3x + 5/2

In the general form of a quadratic, y = ax² + bx + c, c represents the y-intercept.

So, the y-intercept for this equation is 5/2.

 

To find the x-intercepts, let y = 0 and solve for x.

0 = (-1/2)x²- 3x + 5/2   Multiply both sides of the equation by -2.

0 = x² + 6x - 5    Then, use the quadratic formula to solve for x.

x = [-6 ± √(36 + 20)]/2 = [-6 ± √56)/2 = [-6 ± 2√14)/2

x = -3 ± √14

x ≈ .7416     and    x ≈ -6.7416

 

To find the axis of symmetry, use x = -b/2a

x = 3/-1     x = -3

 

To find the vertex, substitute the axis of symmetry into the original formula.

y = (-1/2)(-3)² - 3(-3) + 5/2

y = -9/2 + 9 + 5/2

y = 7

V(-3,7)