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Scilla [17]
3 years ago
14

Hat is the equation of the quadratic function with a vertex at (2,–25) and an x-intercept at (7,0)?

Mathematics
1 answer:
Novosadov [1.4K]3 years ago
8 0

Answer:

y = x² - 4x - 21

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) = (2, - 25), thus

y = a(x - 2)² - 25

To find a substitute (7, 0) into the equation

0 = a(7 - 2)² - 25 = a(5)² - 25 = 25a - 25 ( add 25 from both sides )

25a = 25 ( divide both sides by 25

a = 1, thus

y = (x - 2)² - 25 ← in vertex form

Expand and simplify

y = x² - 4x + 4 - 25

y = x² - 4x - 21 ← in standard form

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What is the equation of the quadratic graph with a focus of (-4,17/8) and a directrix of y=15/8
Temka [501]
So hmm notice the graph below

based on where the focus point is at, and the directrix, then, the parabola is opening upwards, meaning the squared variable is the "x"

\bf \begin{array}{llll}
(y-{{ k}})^2=4{{ p}}(x-{{ h}}) \\\\
\boxed{(x-{{ h}})^2=4{{ p}}(y-{{ k}})}\\
\end{array}
\qquad 
\begin{array}{llll}
vertex\ ({{ h}},{{ k}})\\\\
{{ p}}=\textit{distance from vertex to }\\
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\end{array}

now, keep in mind, the vertex is at coordinates h,k
the vertex itself is half-way between the focus and directrix
the directrix is at y=15/8 and the focus is at y=17/8
so, half-way will then be \bf \cfrac{17}{8}-\cfrac{15}{8}=\cfrac{2}{8}\iff \cfrac{1}{4}

well, so is 1/4 between the focus point and the directrix, half of that is 1/8
so, if you move from the focus point 1/8 down, you'll get the y-coordinate for the vertex, or 1/8 up from the directrix, since the vertex is equidistant to either

what's the "p" distance? well, we just found it, is just 1/8

so, the x-coordinate is obviously -4, get the y-coordinate by 17/8 - 1/8   or 15/8 + 1/8

and plug your values (x-h)² = 4p(y-k)   and then solve for "y", that's the equation of the quadratic

4 0
3 years ago
What is x in this equation −4.5= −0.5(x − 7.1)
Umnica [9.8K]

Answer:

x=16.1

Step-by-step explanation:

-4.5= -0.5(x -7.1)

Divide both sides by -0.5

9=x-7.1

Add 7.1 to both sides

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Hope this helps!

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3 years ago
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MariettaO [177]

Answer:

y = 14

Step-by-step explanation:

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3 years ago
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HELP Sam measures the height of 7 different scoops of ice cream. The mean of the heights was 3.8 cm. Which of the following best
OLga [1]

Sam measures the height of 7 different scoops of ice cream. The mean height was 3.8 cm. If all the scoops are evenly distributed, they would all be 3.8 cm tall.

<h3>How to find the mean value of a data set?</h3>

The mean value of the data set is the ratio of the sum of the data set's values to the number of values it has.

If the data set consists of values

x_1, x_2, ..., x_n

, then we get the mean value as:

\overline{x} = \dfrac{x_1 + x_2 + \cdots + x_n}{n}

Sam measures the height of 7 different scoops of ice cream. The mean height was 3.8 cm.

\overline{x} = \dfrac{x_1 + x_2 + \cdots + x_n}{n}

mean=\dfrac{(a+b+c+d+e+f+g)}{7}

Therefore, If all the scoops are evenly distributed, they would all be 3.8 cm tall.

Learn more about mean;

brainly.com/question/23008823

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