Answer:
Step-by-step explanation:-16x^2 + 24x + 16 = 0.
A. Divide by 8:
-2x^2 + 3x + 2 = 0, A*C = -2*2 = -4 = -1 * 4. Sum = -1 + 4 = 3 = B, -2x^2 + (-x+4x) + 2 = 0,
(-2x^2-x) + (4x+2) = 0,
-x(2x+1) + 2(2x+1) = 0,
(2x+1)(-x+2) = 0, 2x+1 = 0, X = -1/2. -x+2 = 0, X = 2.
X-intercepts: (-1/2,0), (2,0).
B. Since the coefficient of x^2 is negative, the parabola opens downward. Therefore, the vertex is a maximum.
Locate the vertex: h = Xv = -B/2A = -24/-32 = 3/4, Plug 3/4 into the given Eq to find k(Yv). K = -16(3/4)^2 + 16(3/4) + 16 = 19. V(h,k) = V(3/4,19).
C. Choose 3 points above and below the vertex for graphing. Include the points calculated in part A which shows where the graph crosses the x-axis.
Answer:
Step-by-step explanation:
let's firstly convert both fractions with the same denominator, by simply <u>multiplying each fraction by the other's denominator</u>, let's proceed.
![\bf -\cfrac{3}{4}\cdot \cfrac{3}{3}\implies \boxed{-\cfrac{9}{12}}~\hfill -\cfrac{1}{3}\cdot \cfrac{4}{4}\implies \boxed{-\cfrac{4}{12}} \\\\[-0.35em] ~\dotfill\\\\ \boxed{-\cfrac{9}{12}}~~,~~\stackrel{-\frac{2}{3}}{-\cfrac{8}{12}}~~,~~-\cfrac{7}{12}~~,~~\stackrel{-\frac{1}{2}}{-\cfrac{6}{12}}~~,~~-\cfrac{5}{12}~~,~~\boxed{-\cfrac{4}{12}}](https://tex.z-dn.net/?f=%5Cbf%20-%5Ccfrac%7B3%7D%7B4%7D%5Ccdot%20%5Ccfrac%7B3%7D%7B3%7D%5Cimplies%20%5Cboxed%7B-%5Ccfrac%7B9%7D%7B12%7D%7D~%5Chfill%20-%5Ccfrac%7B1%7D%7B3%7D%5Ccdot%20%5Ccfrac%7B4%7D%7B4%7D%5Cimplies%20%5Cboxed%7B-%5Ccfrac%7B4%7D%7B12%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cboxed%7B-%5Ccfrac%7B9%7D%7B12%7D%7D~~%2C~~%5Cstackrel%7B-%5Cfrac%7B2%7D%7B3%7D%7D%7B-%5Ccfrac%7B8%7D%7B12%7D%7D~~%2C~~-%5Ccfrac%7B7%7D%7B12%7D~~%2C~~%5Cstackrel%7B-%5Cfrac%7B1%7D%7B2%7D%7D%7B-%5Ccfrac%7B6%7D%7B12%7D%7D~~%2C~~-%5Ccfrac%7B5%7D%7B12%7D~~%2C~~%5Cboxed%7B-%5Ccfrac%7B4%7D%7B12%7D%7D)
62.25 + 1 - 1 cause that's just 62.25 + 0 which is 62.25
