How do you find the vertex and the intercepts for #y = 4x^2 -8x + 10#?

Answer 1

Vertex (1, 6)
No x-intercepts.

#y = 4x^2 - 8x + 10# x-coordinate of vertex: #x = -b/(2a) = 8/8 = 1# y-coordinate of vertex: y(1) = 4 - 8 + 10 = 6 Vertex( 1, 6). To find the 2 x-intercepts, solve y = 0 by the quadratic formula. #D = b^2 - 4ac = 64 - 160 = - 96#. Because D < 0, there are no real roots (no x-intercepts). The parabola graph doesn't intersect with the x-axis. The parabola opens upward (a > 0). The parabola graph stays completely above the x-axis. graph{4x^2 - 8x + 10 [-20, 20, -10, 10]}
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Answer 2

To find the vertex of the quadratic function y = 4x^2 - 8x + 10, you can use the formula for the x-coordinate of the vertex, which is given by x = -b/(2a), where 'a' is the coefficient of the x^2 term and 'b' is the coefficient of the x term. Substituting the values from the equation, you get x = -(-8)/(2*4) = 1. Plug this value of x back into the original equation to find the y-coordinate of the vertex.

To find the x-intercepts (also known as roots or zeros), set y = 0 and solve the resulting quadratic equation 4x^2 - 8x + 10 = 0 using the quadratic formula or factoring.

To find the y-intercept, simply plug in x = 0 into the equation y = 4x^2 - 8x + 10 and solve for y.

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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.

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.

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.

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.

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