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andrezito [222]
2 years ago
13

What is the relationship between the discriminant of a quadratic and its graph?

Mathematics
1 answer:
faltersainse [42]2 years ago
4 0

Answer:

In a quadratic equation of the shape:

y = a*x^2 + b*x + c

we hate that the discriminant is equal to:

D =  b^2 - 4*a*c

This thing appears in the Bhaskara's formula for the roots of the quadratic equation:

x = \frac{-b +-\sqrt{b^2 - 4ac} }{2a}

You can see that the determinant is inside a square root, this means that if D is smaller than zero we will have imaginary roots (the graph never touches the x-axis)

If D = 0, the square root term dissapear, and this implies that both roots of the equation are the same, this means that the graph touches the x axis in only one point, wich coincides with the minimum/maximum of the graph)

If D > 0 we have two different roots, so the graph touches the x-axis in two different points.

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2 years ago
3/2 ( x - 2 ) - 5 = 19
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Answer:

x = 18

Step-by-step explanation:

Distribute 3/2 inside the parentheses

3/2x - 3 - 5 = 19

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3/2x - 8 = 19

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4 0
3 years ago
Read the proof. Given: m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100° Prove: △HKJ ~ △LNP Statement Reason 1. m∠H = 30°, m∠J = 50°,
motikmotik

Answer:

 2. m\angle H+m\angle J +m\angle K =180^{\circ}

Reason: the sum of all interior angles of any triangle is equal to 180º.

Step-by-step explanation:

1) Organizing

Statement  1. m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100° 1. Reason: given

2) Since the sum of all internal angles of any triangle is equal to 180º, just like the formula. N the number of sides of a triangle:

S_{i}=180^{\circ}(n-2)\rightarrow 180(3-2) \therefore S_{i}=180^{\circ}

3) We can also say

m\angle K=180^{\circ}-(m\angle H+m\angle J)\\m\angle  K=180^{\circ}-\left ( 30^{\circ}+50^{\circ} \right )\\m\angle K=100^{\circ}

Similarly to the other triangle:

m\angle L=180^{\circ}-(m\angle N+m\angle P)\\m\angle L=180^{\circ}-\left ( 100^{\circ}+50^{\circ} \right )\\m\angle L=30^{\circ}

4) Hence,

2. m\angle H+m\angle J +m\angle K =180

Reason: The sum of interior angles is equal to 180º.

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Answer:

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Step-by-step explanation:

7 0
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Read 2 more answers
Find the volume of this object.
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Cylinder: 1²(3) = 3
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Prism: 4x3x6 =72

Total: 72+27 = 99in³
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