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1 year ago

What is the standard form of a quadratic function passing through the points (2,4) , (3,5) and (4,3)

Mathematics

1 answer:

Sladkaya [172]1 year ago

5 0

The standard form of a quadratic function is y = 3/2x² + 17/2x - 7

<h3>How to determine the quadratic equation?</h3>

From the question, the points on the quadratic equation are given as

(2,4), (3,5) and (4,3)

The standard form of a quadratic equation is represented as

y = ax² + bx + c

So, we have

Point (2,4):

4a + 2b + c = 4

Point (3,5):

9a + 3b + c = 5

Point (4,3):

16a + 4b + c = 3

Solving using an online calculator. we have

a = 3/2, b = 17/2 and c = -7

Substitute a = 3/2, b = 17/2 and c = -7 in y = ax² + bx + c

y = 3/2x² + 17/2x - 7

Hence, the equation is y = 3/2x² + 17/2x - 7

Read more about quadratic equation at

brainly.com/question/1214333

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Solve the following inequality: |3x|>x+20

nikdorinn [45]

Answer:

x>10,x<−5

Step-by-step explanation:

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3 years ago

PLZ HELP IM 100% LOST ON THIS

xenn [34]

The equation $f(x)=g(x)$ is

$|x-4|-11=-\sqrt{5x}$

Some observations:

$\sqrt{5x}$ is defined only as long as $5x\ge0$ , or $x\ge0$
wherever $\sqrt{5x}$ is defined, its value must be non-negative, so that $-\sqrt{5x}$ is never positive
by the definition of absolute value, we have $|x-4|=x-4$ if $x\ge4$ , and $|x-4|=-(x-4)=4-x$ if $x$ . Then

$|x-4|-11=\begin{cases}x-15&\text{for }x\ge4\\-x-7&\text{for }x$

If $x$ , the equation becomes

$-x-7=-\sqrt{5x}\implies x+7=\sqrt{5x}$

Taking the square of both sides gives

$(x+7)^2=\left(\sqrt{5x}\right)^2\implies x^2+14x+49=5x\implies x^2+9x+49=0$

but since the discriminant is $9^2-4\cdot1\cdot49$ , there are no real solutions.

If $x\ge4$ , then

$x-15=-\sqrt{5x}$

Taking squares gives

$(x-15)^2=\left(-\sqrt{5x}\right)^2\implies x^2-30x+225=5x$

and solving by the quadratic formula gives two potential solutions,

$x=\dfrac{35\pm5\sqrt{13}}2$

which have approximate values of 8.49 and 26.51.

We know for any value of $x$ that $g(x)\le0$ . We have $f(8.49)\approx-6.51$ and $f(26.51)\approx11.51$ , so only the first solution 8.49 is valid.