Hello.
Firstly, we need to simplify the function:
![\mathsf{f(x) = (3x - 5) \times (x + 9)} \\ \\ \mathsf{f(x) = 3x^{2} - 5x + 27x - 45} \\ \\ \mathsf{f(x) = 3x^{2} + 22x - 45}](https://tex.z-dn.net/?f=%5Cmathsf%7Bf%28x%29%20%3D%20%283x%20-%205%29%20%5Ctimes%20%28x%20%2B%209%29%7D%20%5C%5C%20%5C%5C%20%5Cmathsf%7Bf%28x%29%20%3D%203x%5E%7B2%7D%20-%205x%20%2B%2027x%20-%2045%7D%20%5C%5C%20%5C%5C%20%5Cmathsf%7Bf%28x%29%20%3D%203x%5E%7B2%7D%20%2B%2022x%20-%2045%7D)
The graph crosses the 'x' axis when y = 0. Ergo:
![\mathsf{3x^{2} + 22x - 45 = 0} \\ \\ \\ \mathsf{\triangle = b^{2} - 4ac} \\ \\ \mathsf{\triangle = 484 - 4 \times 3 \times (-45)} \\ \\ \mathsf{\triangle = 484 + 540} \\ \\ \mathsf{\triangle = 1024} \\ \\ \\ \mathsf{x = \dfrac{-b \pm \sqrt{\triangle}}{2a}} \\ \\ \\ \mathsf{x_{1} = \dfrac{-22 + 32}{6} = \dfrac{10}{6} = \dfrac{5}{3}} \\ \\ \\ \mathsf{x_{2} = \dfrac{-22 - 32}{6} = \dfrac{-54}{6} = -9}](https://tex.z-dn.net/?f=%5Cmathsf%7B3x%5E%7B2%7D%20%2B%2022x%20-%2045%20%3D%200%7D%20%5C%5C%20%5C%5C%20%5C%5C%20%5Cmathsf%7B%5Ctriangle%20%3D%20b%5E%7B2%7D%20-%204ac%7D%20%5C%5C%20%5C%5C%20%5Cmathsf%7B%5Ctriangle%20%3D%20484%20-%204%20%5Ctimes%203%20%5Ctimes%20%28-45%29%7D%20%5C%5C%20%5C%5C%20%5Cmathsf%7B%5Ctriangle%20%3D%20484%20%2B%20540%7D%20%5C%5C%20%5C%5C%20%5Cmathsf%7B%5Ctriangle%20%3D%201024%7D%20%5C%5C%20%5C%5C%20%5C%5C%20%5Cmathsf%7Bx%20%3D%20%5Cdfrac%7B-b%20%5Cpm%20%5Csqrt%7B%5Ctriangle%7D%7D%7B2a%7D%7D%20%5C%5C%20%5C%5C%20%5C%5C%20%5Cmathsf%7Bx_%7B1%7D%20%3D%20%5Cdfrac%7B-22%20%2B%2032%7D%7B6%7D%20%3D%20%5Cdfrac%7B10%7D%7B6%7D%20%3D%20%5Cdfrac%7B5%7D%7B3%7D%7D%20%5C%5C%20%5C%5C%20%5C%5C%20%5Cmathsf%7Bx_%7B2%7D%20%3D%20%5Cdfrac%7B-22%20-%2032%7D%7B6%7D%20%3D%20%5Cdfrac%7B-54%7D%7B6%7D%20%3D%20-9%7D)
Therefore, the graph crosses the x axis when x = -9 and 5/3.
Hope I helped.
The expression y = 4.998 ·
is the exponential function that passes through the points (- 1, 5 / 3) and (3, 135).
<h3>How to derive an exponential function that passes through two given points</h3>
Herein we find the location of two points set on Cartesian plane that belongs to an exponential function of the form:
![y = A \cdot e^{B \cdot x}](https://tex.z-dn.net/?f=y%20%3D%20A%20%5Ccdot%20e%5E%7BB%20%5Ccdot%20x%7D)
Where:
- A - y-Intercept of the exponential function.
- B - Growth factor
- x - Independent variable.
- y - Dependent variable.
Which is equivalent to the following logarithmic expression:
㏑ y = ㏑ A + B · x
If we know that (x₁, y₁) = (- 1, 5 / 3) and (x₂, y₂) = (3, 135), then the following system of equations is generated:
㏑ (5 / 3) = ㏑ A - B
㏑ 135 = ln A + 3 · B
Then, we solve the system by numerical methods:
㏑ A = 1.609 (A = 4.998), B = 1.098
And the exponential function is equal to y = 4.998 ·
.
To learn more on exponential functions: brainly.com/question/11487261
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Answer: the line is intercepting with 4 if that's what you're asking
Step-by-step explanation:
vertex form of a parabola
y= a(x-h)^2 +k
y =a(x--3)^2 +2
y = a(x+3)^2 +2
Choice B