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Sagot :
[tex]\\ \sf\longmapsto y=-5x^2-6x+15/2[/tex]
[tex]\\ \sf\longmapsto -5x^2-6x-y+15/2=0[/tex]
- Multiply 2 with each term
[tex]\\ \sf\longmapsto -10x^2-12x-2y+15=0[/tex]
- Convert to vertex form
[tex]\\ \sf\longmapsto y=-5(x^2+\dfrac{6}{5}x+\dfrac{9}{25})+\dfrac{93}{10}[/tex]
[tex]\\ \sf\longmapsto y=-5(x^2+2\dfrac{3}{5}x+(\dfrac{3}{5})^2)+\dfrac{93}{10}[/tex]
[tex]\\ \sf\longmapsto y=-5(x+\dfrac{3}{5})^2+\dfrac{93}{10}[/tex]
Compare to vertex form of parabola
[tex]\boxed{\sf y=a(x-h)^2+k}[/tex]
Now
- h=-3/5
- k=93/10
Answer:
- (- 0.6, 9.3)
Step-by-step explanation:
Given parabola:
- y = -5x² - 6x + 15/2
The vertex is determined by x = - b/2a:
- x = - (-6)/(2*(-5)) = -0.6
Find y- coordinate of vertex:
- y = - 5(0.6)² - 6(- 0.6) + 15/2 = 9.3
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