Identifying Slope at a Point - Math

Card 0 of 4

Question

Find the slope of the line tangent to the -intercept of the parabola:

Answer

To find the slope of a line tangent to a parabola at a specific point, find the derivative of the parabola's equation, then substitute the -coordinate of the specific point in the new equation.

In this case, it helps to expand the equation before taking the derivative:

$y = (x+2)^2 - 4 \rightarrow y = (x^2 + 4x +4) - 4 \rightarrow y= x^2 +4x$

Now take the derivative of the expanded equation:

$\rightarrow y^{\prime} = 2x + 4$

Since the -intercept is the point where the -coordinate is , substitute into the equation for .

$y' = 2(0) + 4 \Rightarrow 4$

Compare your answer with the correct one above

Question

Find the slope of the line tangent to the -intercept of the parabola:

Answer

To find the slope of a line tangent to a parabola at a specific point, find the derivative of the parabola's equation, then substitute the -coordinate of the specific point in the new equation.

In this case, it helps to expand the equation before taking the derivative:

$y = (x+2)^2 - 4 \rightarrow y = (x^2 + 4x +4) - 4 \rightarrow y= x^2 +4x$

Now take the derivative of the expanded equation:

$\rightarrow y^{\prime} = 2x + 4$

Since the -intercept is the point where the -coordinate is , substitute into the equation for .

$y' = 2(0) + 4 \Rightarrow 4$

Compare your answer with the correct one above

Question

Find the slope of the line tangent to the -intercept of the parabola:

Answer

To find the slope of a line tangent to a parabola at a specific point, find the derivative of the parabola's equation, then substitute the -coordinate of the specific point in the new equation.

In this case, it helps to expand the equation before taking the derivative:

$y = (x+2)^2 - 4 \rightarrow y = (x^2 + 4x +4) - 4 \rightarrow y= x^2 +4x$

Now take the derivative of the expanded equation:

$\rightarrow y^{\prime} = 2x + 4$

Since the -intercept is the point where the -coordinate is , substitute into the equation for .

$y' = 2(0) + 4 \Rightarrow 4$

Compare your answer with the correct one above

Question

Find the slope of the line tangent to the -intercept of the parabola:

Answer

To find the slope of a line tangent to a parabola at a specific point, find the derivative of the parabola's equation, then substitute the -coordinate of the specific point in the new equation.

In this case, it helps to expand the equation before taking the derivative:

$y = (x+2)^2 - 4 \rightarrow y = (x^2 + 4x +4) - 4 \rightarrow y= x^2 +4x$

Now take the derivative of the expanded equation:

$\rightarrow y^{\prime} = 2x + 4$

Since the -intercept is the point where the -coordinate is , substitute into the equation for .

$y' = 2(0) + 4 \Rightarrow 4$

Compare your answer with the correct one above

Tap the card to reveal the answer