<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.
Answer:
Step-by-step explanation:
If you have trouble working with the coordinate numbers, it can be helpful to plot them on a graph so that you can count grid squares. (see attached)
__
The translation is ...
A' -A = (2, 3) -(3, -4) = (2-3, 3-(-4)) = (-1, 7)
Since positive numbers are to the right or up, negative numbers are to the left or down.
The translation (-1, 7) means a translation 1 unit left and 7 units up.
1,159cm^2 that is the answer
Good morning,
Answer:
![\frac{\sqrt{3} }{2} a](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D%20a)
Step-by-step explanation:
h = altitude
side = a
using Pythagorean theorem: in the right triangle:
h² = a² - (a/2)²
= a² - a²/4
= 3/4a²
= [(√3/2)×a]²
⇒ h = (√3/2)×a.
:)
You can find equivalent ratios by multiplying or dividing both sides by the same number. This is similar to finding equivalent fractions. Some examples of finding equivalent ratios are shown on the right. All the ratios in the diagram are equivalent.