If written out it will look like this 1 + 4 * x
{\text{Direction of parabola depends on the sign of quadratic coefficient of a }} \hfill \\
{\text{quadratic equation}}. \hfill \\
{\text{For given quadratic equation}}. \hfill \\
a{x^2} + bx + c = 0 \hfill \\
{\text{The parabola is in the upward direction if }}a{\text{ }} > {\text{ }}0{\text{ and in downward direction if }}a < 0 \hfill \\
{\text{Here, the equation of given parabola is }} \hfill \\
{x^2} - 6x + 8 = y \hfill \\
\Rightarrow y = \left( {{x^2} - 6x + 9} \right) - 9 + 8 \hfill \\
\Rightarrow y = {\left( {x - 3} \right)^2} - 1. \hfill \\
{\text{Thus, the parabola is in the upward direction}} \hfill \\
Answer:
7.5 30
45 180
Step-by-step explanation:
The given line has x = 1.25 and y = 5.
y/x = 5/1.25 = 4
x is multiplied by 4 to get y since 1.25 * 4 = 5.
That means the equation is
y = 4x
For a proportional function, every value of x must be multiplied by 4 to get y.
x = 7.5
y = 4x = 4(7.5) = 30
We need to find the values for the last line.
11 * 4 = 44
There is no 44
13.75 * 4 = 55
There is no 55.
17.5 * 4 = 70
There is no 70
30 * 4 = 120
There is no 120.
45 * 4 = 180
There is a 180.
a. attached graph; zero real: 2
b. p(x) = (x - 2)(x + 3 + 3i)(x + 3 - 3i)
c. the solutions are 2, -3-3i and -3+3i
p(x) = x³ + 4x² + 6x - 36
a. Through the graph, we can see that 2 is a real zero of the polynomial p. We can also use the Rational Roots Test.
p(2) = 2³ + 4.2² + 6.2 - 36 = 8 + 16 + 12 - 36 = 0
b. Now, we can use Briott-Ruffini to find the other roots and write p as a product of linear factors.
2 | 1 4 6 -36
1 6 18 0
x² + 6x + 18 = 0
Δ = 6² - 4.1.18 = 36 - 72 = -36 = 36i²
√Δ = 6i
x = -6±6i/2 = 2(-3±3i)/2
x' = -3-3i
x" = -3+3i
p(x) = (x - 2)(x + 3 + 3i)(x + 3 - 3i)
38.25
4.25x9