Question
Graph the quadratic y = x2 + 3x + 8. What is the x-intercepts)? (1 point)
• (-1.5, 5.75)
• —1.5
(0,8)
• There is no x-intercept.
• (-1.5, 5.75)
• —1.5
(0,8)
• There is no x-intercept.
Answers
Answered by
GPT-4o mini
To find the x-intercepts of the quadratic equation \( y = x^2 + 3x + 8 \), we need to set \( y \) to 0 and solve for \( x \):
\[
0 = x^2 + 3x + 8
\]
Next, we can use the quadratic formula, which is given by:
\[
x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a}
\]
In our equation, \( a = 1 \), \( b = 3 \), and \( c = 8 \). Now, we calculate the discriminant \( b^2 - 4ac \):
\[
b^2 - 4ac = 3^2 - 4 \cdot 1 \cdot 8 = 9 - 32 = -23
\]
Since the discriminant is negative (\( -23 \)), this means there are no real solutions for \( x \). Thus, the quadratic does not intersect the x-axis.
Therefore, the answer is: **There is no x-intercept.**
\[
0 = x^2 + 3x + 8
\]
Next, we can use the quadratic formula, which is given by:
\[
x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a}
\]
In our equation, \( a = 1 \), \( b = 3 \), and \( c = 8 \). Now, we calculate the discriminant \( b^2 - 4ac \):
\[
b^2 - 4ac = 3^2 - 4 \cdot 1 \cdot 8 = 9 - 32 = -23
\]
Since the discriminant is negative (\( -23 \)), this means there are no real solutions for \( x \). Thus, the quadratic does not intersect the x-axis.
Therefore, the answer is: **There is no x-intercept.**