The correct answer is
y= 0.5(x + 1)^2 -6
The resolution is in the attached photo
Answer:
2
Step-by-step explanation:
given the difference of twice a number and one is three to find "number" let the number be x
2x - 1 =3
2x = 4
x= 2
thus the number is 2
<h2>
1. y-intercept</h2>
![\boxed{(0,-10)}](https://tex.z-dn.net/?f=%5Cboxed%7B%280%2C-10%29%7D)
The quadratic function
represents a parabola. In fact, the graph of a quadratic function is a special type of U-shaped curve called a parabola. To find the y intercept, we set
as follows:
![f(x)=2x^2-8x-10 \\ \\ If \ x=0 \rightarrow f(0)=-10 \\ \\ Then \ y-intercept: \\ \\ (0,-10)](https://tex.z-dn.net/?f=f%28x%29%3D2x%5E2-8x-10%20%5C%5C%20%5C%5C%20If%20%5C%20x%3D0%20%5Crightarrow%20f%280%29%3D-10%20%5C%5C%20%5C%5C%20Then%20%5C%20y-intercept%3A%20%5C%5C%20%5C%5C%20%280%2C-10%29)
<h2>
2. x-intercepts</h2>
![\boxed{(-1,0) \ and \ (5,0)}](https://tex.z-dn.net/?f=%5Cboxed%7B%28-1%2C0%29%20%5C%20and%20%5C%20%285%2C0%29%7D)
To find the other x-intercept, we must set
as follows:
![f(x)=2x^2-8x-10 \\ \\ If \ y=0 \rightarrow 2x^2-8x-10=0 \\ \\ Using \ the \ quadratic \ formula: \\ \\ x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ \therefore x=\frac{-(-8) \pm \sqrt{(-b)^2-4(2)(-10)}}{2(2)} \\ \\ \therefore x_{1}=-1 \ and \ x_{2}=5](https://tex.z-dn.net/?f=f%28x%29%3D2x%5E2-8x-10%20%5C%5C%20%5C%5C%20If%20%5C%20y%3D0%20%5Crightarrow%202x%5E2-8x-10%3D0%20%5C%5C%20%5C%5C%20Using%20%5C%20the%20%5C%20quadratic%20%5C%20formula%3A%20%5C%5C%20%5C%5C%20x%3D%5Cfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%20%5C%5C%20%5C%5C%20%5Ctherefore%20x%3D%5Cfrac%7B-%28-8%29%20%5Cpm%20%5Csqrt%7B%28-b%29%5E2-4%282%29%28-10%29%7D%7D%7B2%282%29%7D%20%5C%5C%20%5C%5C%20%5Ctherefore%20x_%7B1%7D%3D-1%20%5C%20and%20%5C%20x_%7B2%7D%3D5)
Therefore, the other x-intercept is
. You can see both the y-intercept and the x-intercepts in the figure below.
You move the decimal point forward until it reaches the one so it looks like this:
1.4 x 10⁵
the exponent, 5, just tells you how many spaces the decimal point moved.