Answered: "Where does the graph of y=2x2+x−15 cross the..."

GrareeCowui

Answered question

2022-01-21

Where does the graph of

y = 2 x^{2} + x - 15

cross the x-axis?

waijazar1

Beginner2022-01-22Added 13 answers

Step 1
Cutting the x axis means

y = 0

Which means

2 x^{2} + x - 15 = 0

We are going to seek the

Δ

:
The equation is of the form

a x^{2} + b x + c = 0

a = 2; b = 1; c = - 15

Δ = b^{2} - 4 a c

Δ = 1^{2} - 4 \times 2 \times (- 15)

Δ = 1 + 120

Δ = 121 = (\sqrt{11})

x_{1} = \frac{- b - \sqrt{Δ}}{2 a}

x_{1} = \frac{- 1 - 11}{4}

x_{1} = - \frac{12}{4}

x_{1} = - 3

x_{2} = \frac{- b + \sqrt{Δ}}{2 a}

x_{2} = \frac{- 1 + 11}{4}

x_{2} = \frac{10}{4}

x_{2} = \frac{5}{2}

Thus, the function cuts the x axis in

x = - 3

and

x = \frac{5}{2}

NKS graph

{2 x^{2} + x - 15 [- 10, 10, - 5, 5]}

porekalahr

Beginner2022-01-23Added 10 answers

Step 1

y = 2 x^{2} + x - 15

= (2 x - 5) (x + 3)

y = 0

when

x = \frac{5}{2}

x = - 3

so the graph crosses the x-axis at

(- 3, 0)

and

(\frac{5}{2}, 0)

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