Answer:
y = 
x² - 7
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (0, - 7), thus
y = a(x - 0)² - 7
To find a substitute (4, - 3) into the equation
- 3 = a(4 - 0)² - 7, that is
- 3 = 16a - 7 ( add 7 to both sides )
4 = 16a ( divide both sides by 16 )
a = , thus
y = x² - 7
X=-1/2 that is the answer
Answer:
x = 4, x = 8
Step-by-step explanation:
To find the roots equate to zero, that is
- x² + 12x - 32 = 0 ( multiply through by - 1 )
x² - 12x + 32 = 0
Consider the factors of the constant term (+ 32) which sum to give the coefficient of the x- term (- 12)
The factors are - 4 and - 8, since
- 4 × - 8 = + 32 and - 4 - 8 = - 12, thus
(x - 4)(x - 8) = 0
Equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x - 8 = 0 ⇒ x = 8
