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Makovka662 [10]
3 years ago
7

Which point is the vertex of the quadratic function f(x)=x2−6x+8?

Mathematics
2 answers:
olya-2409 [2.1K]3 years ago
4 0
(3,-1)
It needs to be written in standard form before you try to solve it.

jarptica [38.1K]3 years ago
4 0

Another method!

<span><span>Pvertex</span>→<span>(x,y)</span>→<span>(4,9)</span></span>

Explanation:

Given:<span> y=<span>x2</span>−8x+7</span>

This is already in the form <span> y=a<span>(<span>x2</span>+<span>ba</span>)</span>+c as a=1</span>

So we can do this 'trick'

Applying <span><span>x vertex</span>=<span>(−<span>12</span>)</span><span>(<span>ba</span>)</span>→<span>(−<span>12</span>)</span><span>(−8)</span>=+4</span>

<span>To determine <span>yvertex</span></span>

Substitute for <span>x=<span>(−4)</span></span> in the original equation giving:

<span> <span>yvertex</span>=<span><span>(4)</span>2</span>−8<span>(4)</span>+7</span>

<span><span>y vertex</span>=+16−32+7=−<span>9
</span></span>

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Drag each tile to the correct box. not all tiles will be used.
lana66690 [7]

Answer:

y=\frac{13}{6}x             y= \frac{11}{5}x          y = \frac{21}{9}x          y = \frac{19}{8}x

Step-by-step explanation:

Given

The attached graph

Required

Equations with higher unit rate

First, calculate the unit rate of the graph

m = \frac{y_2 - y_1}{x_2 - x_1}

Where:

(x_1.y_1) = (0,0)

(x_2.y_2) = (7,15)

So:

m = \frac{15 - 0}{7 - 0}

m = \frac{15}{7}

m = 2.143

For the given options.

The unit rate is the coefficient of x

So: y = \frac{19}{8}x

Going by the above definition of unit rate.

m = \frac{19}{8}

m = 2.375

y = \frac{27}{13}x

m = \frac{27}{13}

m = 2.077

y = \frac{21}{9}x

m = \frac{21}{9}

m = 2.333

y= \frac{11}{5}x

m= \frac{11}{5}

m= 2.20

y = \frac{15}{7}x

m = \frac{15}{7}

m = 2.143

y = \frac{31}{15}x

m = \frac{31}{15}

y = 2.067

y=\frac{13}{6}x

m=\frac{13}{6}

m=2.167

The unit rates grater than the graph's from small to large are:

y=\frac{13}{6}x             y= \frac{11}{5}x          y = \frac{21}{9}x          y = \frac{19}{8}x

m=\frac{13}{6}              m= \frac{11}{5}           m = \frac{21}{9}            m = \frac{19}{8}

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3 years ago
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Please Help!!! WILL GIVE BRAINLIEST!!!
kompoz [17]

Answer:

The correct statements are:

A) This polynomial has a degree of 2, so the equation x^{2}  + 4x + 4has exactly two roots.

B: The quadratic equation x^{2}  + 4x + 4 has one real solution, x=−2, and therefore has one real root with a multiplicity of 2.

Step-by-step explanation:

Here, the given polynomial is  f(x) = x^{2}  + 4x + 4

FUNDAMENTAL THEOREM OF ALGEBRA:

If P(x) is a polynomial of degree n ≥ 1, then P(x) = 0 has exactly n roots, including multiple and complex roots.

Now, here the given polynomial is a quadratic polynomial with degree 2.

So, by the fundamental theorem, f(x) has EXACTLY 2 roots including multiple and complex roots.

Now, solving the equation , we get that the only possible roots of the polynomial p(x) is x = -2 and x = -2

So, f(x) has only one distinct root x = -2 with a multiplicity 2.

Hence, the correct statements are:

A) This polynomial has a degree of 2, so the equation x^{2}  + 4x + 4has exactly two roots.

B: The quadratic equation x^{2}  + 4x + 4 has one real solution, x=−2, and therefore has one real root with a multiplicity of 2.

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makvit [3.9K]

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