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How do you find the vertex and the intercepts for #f(x)= -3x^2-6x-7 #?

Answer 1

Vertex (-1, -4)
y-intercept = - 7

#f(x) = - 3x^2 - 6x - 7# x-coordinate of vertex: #x = - b/(2a) = 6/-6 = - 1# y-coordinate of vertex: f(-1) = - 3 + 6 - 7 = -4 Vertex (-1, -4) To find the 2 x-intercepts, solve the quadratic equation: #f(x) = - 3x^2 - 6x - 7 = 0# #D = d^2 = b^2 - 4ac = 36 - 84 = - 48 < 0# There are no x-intercepts (no real roots) because D < 0. To find y-intercept, make x = 0 y-intercept = - 7. Since a < 0, the parabola graph opens downward and stays completely below the x-axis. graph{- 3x^2 - 6x - 7 [-20, 20, -10, 10]}

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Answer 2

Isaiah Anthony

To find the vertex of the function ( f(x) = -3x^2 - 6x - 7 ), use the formula ( x = -\frac{b}{2a} ) to find the x-coordinate, then substitute it into the function to find the y-coordinate. For the x-intercepts, set ( f(x) = 0 ) and solve for x. For the y-intercept, set ( x = 0 ) and evaluate the function.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.